XXV. Heidruna, wildest of the train,
That sport on hill, or russet plain,
Near Odin's hall falacious breeds,
And on the leaves of Lærad feeds.
His spacious horn shall fill the bowl,
That lifts to rapture Odin's soul;
And ever drinking --- ever dry---
Still the copious stream supply.

The goat, which over the hall of Heriafauthr,
Standeth, and nippeth for food the boughs of Laerath,
Is Heithrun; Skaptker daily shall brim with her milk,
The sparkling mead which never can cease to flow.

25. Heidrun the goat is called,
that stands o’er Odin’s hall,
and bits from Lærad’s branches.
He a bowl shall fill
with the bright mead;
that drink shall never fail.

20. Heathrun is the name of the goat that stands on the hall of
the Father of Hosts and bites at the boughs of Learad (a tree). She
shall fill a vat with pure mead which shall never fail.

25. Sky-bright o'er Valholl stands, the goat,
who gnaws the Shelterer's boughs ;
she fills a bowl with the shining mead :
'Tis a draught which runs not dry.

25. Heithrun is the goat  who stands by Heerfather’s hall,
And the branches of Lærath he bites;
From his horns a stream into Hvergelmir drops,
Thence all the rivers run.

25. Heithrun, the goat    on the hall that stands,
    eateth off Lærath's limbs;
    the crocks she fills with clearest mead,
    will that drink not e'er be drained.

25. Heath-Run is the goat in the hall of All-Father
Who bites at Laerað's boughs:
She shall fill the decanter with clear mead,
That drink shall never run dry:

The goat, Heidrun, stands on Warfather’s hall
And bites off Laerad’s branches;
The cask she fills with the clearest mead
can’t be drunk dry.

25. Heidrun is the goat's name, who stands on Father of Hosts' hall and grazes Lærad's branches;
she will fill a vat of shining mead,
that liquor cannot ever diminish.

25. Shining Rune is the she-goat's name
that stands on the Father of Armies' hall
and browses from Listener's branches.
She will fill a cask of the clear mead-
that drink does not run dry.

25.  ‘Heidrún is the name of the goat
standing on Host-father’s hall
who bites off Lærad’s [the World-tree?] limbs;
she fills a vat with shining mead
a draught that does not diminish.

1923 Henry Bellows in his The Poetic Edda as “Grimnismol: The Ballad of Grimnir”:
 
"The first line in the original is, as indicated in the translation, too long, and various attempts to amend it have been made. Heithrun: the she-goat who lives on the twigs of the tree Lærath (presumably the ash Yggdrasil), and daily gives mead which, like the boar's flesh, suffices for all the heroes in Valhall. In Snorri's Edda Gangleri foolishly asks whether the heroes drink water, whereto Har replies, 'Do you imagine that Othin invites kings and earls and other noble men, and then gives them water to drink?'"

Snorri paraphrases this verse in Gylfaginning 39. His source is clearly Grímnismál 25.

Hyndla compares Freyja to Heidrun, who runs "hot among the he-goats". There is clearly a sexual side to the comparison. The boar/warrior is her lover. The word "riða", as in Freyja 'rides' her lover Ottar, also has a similar meaning in Icelandic slang.  Sexual intercourse is necessary to perpetuate the unending cycle of life necessary to keep Valhall full.

If I may extend the poetic conceit,  I would suggest that the lactating she-goat is representative of a breast-feeding mother. It's yet another symbol in the cycle of regeneration already expressed around the Einherjar. The spiritual rebirth is also a physical birth.  As Heidrun keeps the einherjar hydrated, the lactating mother feeds her newborn infant. At least one modern artist has envisioned Heidrun this way:

The symbolism is consistent and indicative of a regular cycle, a ring with no beginning and no end. Life proliferates.

According to evidence preserved in the work of Jakob Grimm and elsewhere, the boar is a sacred Yuletime (year-end) meal. Yule cakes are made in the shape of boars (cp. modern Christmas cookies). The last sheaf of grain is feed to the Yule boar before it is slaughtered, and the plowman is fed some of the Yule boar's preserved meat in the Spring before plowing in German folk tradition. This connects food-production directly to the annual cycle, and through the boar to the sexual cycle as well. The warrior is compared to the boar (as food). The Yule boar is served up with an apple, the symbol of renewing youth, in its mouth.  The symbols are consistent and interlaced.

We may be touching on the heart of the religious mystery here. Both human and boar have equivalent value in the Germanic symbolism of sacrifice. The boar is thus a powerful symbol in Germanic religion and appears to represent the eternal rebirth of mankind. This interpretation fits well with other examples from the lore.

He-goats draw Thor's car. Like the boar Sæhrimnir they can be slaughtered, eaten and brought to life again, if their bones are laid unbroken on their flayed skins. When the whole heap is hallowed by Thor's hammer (a phallic symbol according to many scholars), the goats stand up again, reborn whole. Thor's goats provide him and his travelling companions (his comrade in arms) a neverending supply of meat. Human flesh is, of course, the "best of meats" (Grímnismál 18). Compared to Sæhrimnir, human flesh is the unending supply opf meat that "feeds'  the Einherjar (i.e. increases their numbers, strengthens them). Similarly, Heidrun, a she-goat, provides a neverending supply of mead (i.e. mother's milk) to the human Einherjar. Those who eat and drink it are reborn anew each day.

These are powerful indicators of a belief in reincarnation. The reversal of gender may be significant as well. Heidun is female, Thor's goats Tooth-gnasher and Tooth-grinder are male. Both meat and mead, both male and female are necessary in the chain of life. It's a natural balance. This may also explain the signifcance of the number three: two opposites unite to create a third.  Man and woman unite to create an infant. Opposites, brought together create a balanced third. In the story of creation, heat and cold flow into the abyss, creating the conditions necessary for life.  The cold well Hvergelmir (male) in the north and the warm well, Urdar brunn (female) in the south are located on opposite sides of Mimir's well, from which "Mimameiðr, "Mimir's Tree" or Yggdrassils askur (the world-tree, cf. Askur, the first man) rises. In Gylfaginning, Snorri informs us that Mimir's well is located "where Ginnungagap once was."

We commonly find gender reversal in contexts where order is upset and must be restored. Consider when Skadi comes to Asgard to avenge her father Thjazi's death. She comes dressed in armor, seeking revenge, as a male heir would. The gods promise to make her laugh and to allow her to choose a husband from their ranks by the beauty of his feet alone. Like female brides who are chosen for the beauty of their faces, the male gods are also veiled. Skadi, the woman, selects her mate. Similarly, to make Skadi laugh, Loki ties his testicles with a cord to the beard of a nanny goat. Each yells out in the ensuing tug of war, until at last Loki falls (naked?) into her lap. Loki thus emasculates himself by tethering his male sex organs to the beard (a male attribute) of a female animal. The reversal of gender is obvious. This reversal restores the balance. Similarly, Thor must go to the giant Thrym's dressed as a bride, impersonating Freyja, to retrieve his stolen hammer. The hammer is often interpreted as a phallic symbol which not only slays the sacrifice and kills giants (who are called 'calves' in Þórsdrápa), but one which is also laid in the lap (i.e. the vagina) of a new bride. The same hammer kills and resurrects (through hallowing) Thor's goats, which are the polar opposite of the goat Heidrun.

The fact that this interpretation incorporates and consistently explains various symbols found in the Germanic religious sphere speaks strongly for its validity.