For me, it's just sensitivity. Like it almost feels like a bruise or something. It doesn't really actively hurt, but it's very sensitive to touch, and when you touch it in the wrong way there's a bit of ouch.
That's most of the time. Admittedly, though, during my last growth spurt, all of a sudden I got this shooting pain in my right nipple where it felt like it was ripping apart from the inside. That's only happened a couple of times, though, and it only lasts for a few seconds before it calms down again.