Fimm hvndrvþ gólfa
oc vm fiorum togum,
svá hygg ek Bilskirrni með bvgom;
ranna þeira
er ek rept vita,
míns veit ek mest magar.  

Fim. h. gólfa
ok um fiorum tigvm,
svá hygg æk a  valhöll vera Bil skirrni með bvgom;
ranna þeira
er ek rept vita,
míns veit ek mest magar.  

Fimm hundruð gólfa
ok umb fjórum tögum,
svá hygg ek Bilskirrni með bugum;
ranna þeira
er ek reft vita,
míns veit ek mest magar.  

 XXIV. Five hundred domes aspiring high,
With forty others pierce the sky:
There, Gods in mazy lab'rynths roam ---
One portal leads to ev'ry dome:
But that which loftiest pillars grace,
Belongs to my illustrious race.

Five hundred and forty, I think, are the spacious halls
That stretch beneath Bilscirni'a winding roof;
Of all the hall-filled piles which I have known,
Greatest, I know, is the palace of my son.

24. Five hundred floors,
and forty eke, I think,
has Bilskirnir with its windings.
Of all the roofed
houses that I know,
is my son’s the greatest.

24. Five hundred rooms        and forty there are
I ween, in Bilskirnir built;
Of all the homes        whose roofs I beheld,
My son’s the greatest meseemed.

24. Five hundred rooms and forty there are
I ween, in Bilskirnir built;
Of all the homes whose roofs I beheld,
My son’s the greatest meseemed.

23. Five hundred rooms  and forty withal
    I ween that in Bilskirnir be;
    of all the halls  which on high are reared
    the greatest I see is my son's.

23. Five hundred and forty doors
are built into Bilskirnir,
Furnished with rings: of roofed halls
The largest belongs to my son.

24. Five hundred daises and forty,
so I think Bilskirnir has in all;
of all those halls which I know to be roofed,
my son's I think is the greatest.

24. Five hundred floors
and about forty more, so I think,
are in Defier of Ruin, all reckoned,
Of those residences
that I know have a roof
the greatest, I am sure, is my son's.

24.  ‘Five hundred floors and forty
I think Bilskírnir has in all;
of all the dwellings that I know with roofs
my son’s I reckon the most.

In R, verses 23 and 24 are reversed. Here, these verses are arranged according to the A manuscript.

The name Bilskirnir only appears twice in Snorri’s Edda. There he quotes the verse from Grímnismál and later in Skáldskaparmál quotes  a skaldic kenning containing the name.
 
Gylfaginning 21:

Based on this skaldic verse, there is little question that Bilskirnir is the name of Thor’s hall. It seems apparent that the Grímnismál poet is making a conscious comparison between Valhall and Bilskirnir. However, I don’t think he is attempting to identify the two places as some have suggested— merely drawing a comparison.
  
The poet of Grímnismál makes it a point to compare Bilskirnir to Valhall, beginning each stanza with nearly identical lines. The lines are so close that one of the transcribers of the poem (either the scribe of Codex Regius, or the scribe of AM 748 I 4to) got their original order confused. The verses are reversed in these— the only manuscript copies of the poem.
 
The comparison may be one of function. At Ragnarok, 800 warriors will issue from each of Valhall's doors to join the battle. Thor accompanies them to the battlefield. The poet intend is probably to highlight the comparison between Thor’s role as the defender of Asgard and the important role of the Einherjar. The Einherjar join Odin when he faces the wolf Fenrir. Thor faces Jormungand, Fenrir’s brother, the Midgard serpent alone. 
 
 Yet, there is some evidence that Thor may face Fenrir as well. In the Codex Regius manuscript of Völuspá 54, the poet says:
 

The passage has no parallel in the Hauksbók manuscript or in the manuscripts of Snorri's Edda. It is also possible that the phrase "Odin's son" inserted here was intended to refer to Vidar, who avenges his father by slaying Fenrir.  However, most translators and scholars generally emend the word “wolf” found there to “orm” ('serpent') since Odin's son Thor is the subject of the verse, and  Snorri informs us that he is to face his traditional enemy Jörmungand, the Midgard serpent  at Ragnarök and not the Fenris wolf.

It is of interest to note that the verse concerning Valhall says that it has 540 doors (dyrr) while Bilskirnir has 540 floors or rooms (golf). Otherwise, each verse begins with the same half-stanza.

1984 Rudolf Simek, Dictionary of Northern Mythology:

Bilskírnir (ON,' the one striking lightning with rays of light').

2002 John Lindow, Handbook of Norse Mythology:

"The meaning of the name is unclear, but it seems to be either 'suddenly illuminated [by lightning]' or 'everlasting'."