Please note, only admins can perform this function.
A pending user is someone who requested access to your library via the Account Registration screen (a Professional and Enterprise accounts have). Admins can activate these account requests by approving them and assigning them a proper permission.
Go the to Admin Tab and choose Users and Permissions.
Click on Pending Users along the lefthand side.
Find the user you are looking for and click on their name.
Assign them a permission level and click Approve. Once you have done this they will be automatically sent an email detailing their account information. They will then be listed in the Active User list.
You may also Decline a pending user if you wish. They will receive no further contact from you in that case.