I can't speak for Target, but generally speaking, "nights" can mean overnight or it can mean afternoon to late evening.
"Overnight," means just that.
You'd most likely work something like 10 pm to 7 am, 11 pm to 8 am, etc.
Or you could have the lovely experience of your cushy daytime job turning into working 7 pm to 7 am because they needed a manager on night shift.
Anyway, overnight is third shift.
The exact hours might vary a bit but suffice it to say that you will get to see the sun come up every morning and then spend the rest of the day trying to sleep while your neighbor is mowing his yard, cutting down a tree with a chainsaw, working on his motorcycle, earnest young Mormons are ringing your doorbell to tell you about Jesus, the mailman is ringing your doorbell with a certified letter from the IRS wanting the 60 bucks you owe them from last year, etc.