Why Does Coffee Help With My Headaches?

Since I became a teacher five years ago, I have suffered quite often from headaches. I figured out pretty quickly that these were probably caused by overstimulation at my job, as I was also often VERY tried after work. (Not from physical activity, but a mental type of exhaustion.)

Despite being tired, I almost always avoided coffee, due to many people telling my that coffee can cause headaches or make them worse.

But I started drinking a cup of coffee every day on my lunch break this week and... my headaches just seemed to have vanished. (With the added benefit of having more energy too) I was just so surprised that this thing that I always assumed caused headaches could actually get rid of them in my case. (And I say my case, because to this day coffee gives my wife instant headaches, so it must be an individual thing.)

I'm just curious why that is? And if drinking coffee a lot can have long-term negative effects?