Letting your lawn go to seed is when your grass is allowed to grow naturally without mowing so that it produces seeds (which covers your lawn with free grass seeds. )
basically not cutting the grass. plants don't go to seed unless they are aloud to fully mature. all they are saying is let the grass go long enough so it will reseed itself.
This means letting the grass grow tall and allowing seeds to develop. When the seeds develop on the grass the tall grass resembles a paint brush. Some people let their grass go to seed so new seeds will drop on the ground grow new grass.