I had intercourse, I took the pill, but my period is late

There is a chance she's pregnant. The morning after pill only works if she hadn't yet ovulated. If she had already ovulated, the pill wouldn't do anything for her. The pill doesn't end a pregnancy that exists, it just prevents ovulation from happening.

However, what is far more likely is that the pill is just delaying her period, which is a very common response. Emergency contraception puts a looooot of one hormone into the body, and sometimes after it just doens't know what to do with itself. Periods can be delayed by a whole cycle. 

If she takes a home pregnancy test, she'll know for sure.