You might have called a restaurant asking to make a reservation only to be told that they do not take them. Many will tell you that they offer Call Ahead or Priority Seating instead.
Typically Call Ahead just means you call to put your name on the waitlist. You call when you are about to leave for the restaurant and tell them you will be there in 20 minutes, please put your name down on the waitlist. It does not mean the table will be ready for you, it just means you will spend less time sitting in the waiting area because your name will already have saved your place in line for you.
Several situations could take place. For instance, you call and say you will be there in 20 minutes, but the current waitlist estimate at the restaurant is 45 minutes. That means you just have to sit in the waiting area for approximately 25 minutes instead of the full 45.
Or you could say you'll be there in 10 minutes and there is an accident, so it actually takes you 30 minutes to arrive. Your name might now be at the top of the list, but the host keeps seating other parties until you arrive and then you get the next table that comes available.
Why do restaurants use Call Ahead seating? Typically it is because they are so busy that they don't want to turn anyone away. Many times restaurants have issues with taking reservations because of no-shows, incorrect reservations, or people who try to game the system by making multiple reservations. This can lead to tables sitting vacant waiting for the reservation party to show up when a restaurant could be making money by seating a party that's already there.
While patrons might see Call Ahead seating as an inconvenience, it's really a compromise between the restaurant and patrons. Restaurants fill tables and patrons have less waiting time.