As the others have mentioned your wait stats will help identify the exact issue.

Without that detail and going on the symptoms it sounds like you most likely have IO contention. Causing queries to take longer to return the results.

As a typical kind of example:

1. Procedure A takes on average 20s to complete when backups are not running.

2. Procedure A takes on Average 30 seconds to complete when backups are running.

By default your application probably has the typical 30 seconds timeout period for database calls, which means when procedure A takes longer than 30 seconds to complete the application will return a time out error as it has given up waiting on the results.

Is your database backup(s) being written to the same physical drive(s) as the database log \ data devices.