There are 9 wayshrines located in oblivion. You should visit the wayshrines to repent to the gods for the evil things you have done. If you fame is greater than your infamy you will be allowed to pray. However if your infamy is greater than your fame the gods will reject you.

Healings

When you pray at a wayshrine the gods heal you of all illnesses. This means that if anything was affecting you before, it will now be gone. For example, if you had the vampire disease and then you prayed you would be cured ( make sure you heal yourself of the vampire disease in the first 3 days or you will become a vampire.)

Effects of Wayshrines

Each of the wayshrines will increase your skills in some way. Here is a list of what each does.

Sources

Image from http://www.imperial-library.info/obbooks/wayshrines.jpg

Information from wayshrines