These are percentages describing what percent of the continent’s dig sites are of that culture. A 25% next to Troll at Northrend would mean that 25% of the dig sites on that continent are Troll. A higher percent indicates a higher chance of getting that dig site on that continent, so that is obviously more desirable and is helpful information if you are hunting a specific faction’s rare. Source

— Updated for Patch 4.1.0

Edit: Updated numbers to reflect the Vashj’ir dig sites removal.

(Numbers were rounded off above in the table)

Dwarf
There is only 1 Dwarf site in Kalimdor compared to 18 (post-450) or 14 (pre-450). No contest on this one, but here are the percents anyway.
Eastern Kingdoms (pre-375): 28.57% (14/49)
Eastern Kingdoms (post-375, pre-450): 27.45% (14/51)
Eastern Kingdoms (post-450): 32.73% (18/55)
Kalimdor (pre-450): 2.08% (1/48)
Kalimdor (post-450): 1.45% (1/62)
Verdict: Eastern Kingdoms (All skill levels)

Fossil
After the removal of the Vashj’ir dig sites, I am forced to recommend Eastern Kingdoms post-450 for Fossil fragments. Before that though, they’re exactly even.
Eastern Kingdoms (pre-450): 26.53% (13/49)
Eastern Kingdoms (post-375, pre-450): 25.49% (13/51)
Eastern Kingdoms (post-450): 23.64% (13/55)
Kalimdor (pre-450): 27.08% (13/48)
Kalimdor (post-450): 18.84% (13/69)
Verdict: Kalimdor (pre-450) and Eastern Kingdoms (post-450)

Night Elf
There are only 2 Night Elf dig sites in Eastern Kingdoms, and just a few more than that in Northrend. On the other hand, over half of Kalimdor is Night Elf.
Eastern Kingdoms (pre-450): 4.08% (2/49)
Eastern Kingdoms (post-375, pre-450): 3.92% (2/51)
Eastern Kingdoms (post-450): 3.64% (2/55)
Kalimdor (pre-450): 62.50% (30/48)
Kalimdor (post-450): 50.72% (35/69)
Northrend: 13.79% (4/29)
Verdict: Kalimdor (All skill levels)

Troll
Troll relics are also in Northrend, so here’s a three-way comparison.
Eastern Kingdoms (pre-450): 40.82% (20/49)
Eastern Kingdoms (post-375, pre-450): 39.22% (20/51)
Eastern Kingdoms (post-450): 36.36% (20/55)
Kalimdor (pre-450): 8.33% (4/48)
Kalimdor (post-450): 5.80% (4/69)
Northrend: 17.24% (5/29)
Verdict: Eastern Kingdoms (all skill levels)

Draenei
This one is easy because there is only one location, but I’ll list it anyway for completion sake and just for fun.
Outland: 53.57% (15/28)
Verdict: Outland

Orc
See above (Draenei).
Outland: 46.43% (13/28)
Verdict: Outland

Nerubian
In addition to upping the number of Nerubian sites in Northrend slightly, Blizzard added two Nerubian sites to Eastern Plaguelands, requiring 375 Archaeology, of course. I’m not going to create a new column in the table just for 375-450 Archaeologists, so you’ll just have to live with the numbers being here!
Eastern Kingdoms (post-375, pre-450): 3.92% (2/51)
Eastern Kingdoms (post-450): 3.64% (2/55)
Northrend: 24.14% (7/29)
Verdict: Northrend

Vrykul
Only one possible area for these.
Northrend: 44.83% (13/29)
Verdict: Northrend

Tol’vir
Only one possible area for these as well, but luckily, Patch 4.0.6 has nearly doubled the amount of Tol’vir sites in Kalimdor.
Kalimdor (post-450): 23.19% (16/69)
Verdict: Kalimdor (post-450)

Tol’vir and Nerubian are the two rarest races to get things from. Luckily, there are only two Nerubian artifacts of any value, so you won’t have worry about them very often.

Also, the information above is based on assumption, like most things in the world. This assumption is that the the number of dig sites of each culture is directly proportional to the chance the dig site is selected. However, this assumption appears to be accurate though. The results appear to justify the assumption (low Tol’vir/Nerubian rates, etc).

Thanks Simca! (Source)