Question:

Two users have the same profile, but different Territories. When they view the same Account, why can one user (A) edit the Account information while the other user (B) cannot?

Answer:

The reason is that user (B) can only view the Accounts assigned to the Territory. But, user (A) can view and edit Accounts assigned to the Territory.

Navigate to: Setup -> Administration Setup -> Manage Territories -> Territory Settings.

This can be confirmed from the Territory Settings: