Wait means ‘stay in the same place or not do something until something else happens’. We can use it with or without for:
Put a tea bag into the cup, then add water and wait (for) a minute or two before taking it out.
I phoned the head office but I had to wait (for) five minutes before I spoke to anyone.
We waited (for) hours to get the tickets.
When we use a direct object after wait, we have to use wait for:
Wait for us outside the cinema. We’ll be there at seven o’clock.
Not: Wait us …
I waited for the postman every day last week hoping that your present would arrive.
Not: I waited the postman …
Wait can be followed by the to-infinitive:
All right, I’ll wait to hear from you, Adam, then I’ll ring Simon.
By 9 pm there were about 20 people still waiting to vote.
When we are very excited about something that is going to happen, we use the phrase can’t wait for + noun phrase or can’t wait + to-infinitive:
I can’t wait for tonight. I’m having a party! (I’m really looking forward to tonight.)
We can’t wait to go to Barcelona in June. (We’re really looking forward to going.)
