Diagnosis
Lint has built up inside the cabinet, around the heating element or gas burner tube, and is burning off.
How to Fix It
Unplug the dryer. Pull it out. Remove the back panel. Use a vacuum with a hose attachment to thoroughly clean all lint from inside the cabinet, especially around the burner assembly and the blower wheel. Also, clean the front bulkhead behind the lint filter housing.
If That Didn't Work
A foreign object like a plastic tag or sock could be stuck against the burner tube or on the blower housing, melting. You'll need to disassemble further to find it.
Heads Up
This smell is a serious warning. Do not ignore it. Continuous lint buildup inside the cabinet is a primary cause of dryer fires.