In most cases, the verb ‘wait’ is followed by the preposition ‘for’. We wait for the bus, we wait for a phone call, we wait for a winning lottery ticket! We also wait for people.
To say, as in this example, ‘I waited on my wife in front of the supermarket’, implies that you were physically on top of her, either sitting or standing on the poor woman. We assume that this was not the case. Instead, you should say, ‘I waited for my wife.’
To wait ‘on’ someone does have a meaning in English. It is the job of a waiter in a restaurant. He waits on tables, meaning he attends to the customers sat on them.
Here’s the two put together:
Customer: Why haven’t you taken our drinks order? We have been waiting for 15 minutes.
Waiter: I’m sorry, sir. We are understaffed tonight, and I have to wait on over 20 tables!