I CAN'T DELETE MY IPHONE MESSAGES?

I've been trying to delete my iphone messages to free up space so I deleted them by swiping them and it didn't work? I restarted my phone and everything.

Sounds like you sent some naughty messages! XD Haha, sometimes when your finger is oily it won't work so easily? Or of it continues, Press the "Home" and "Lock" buttons for about until the phone goes of, (Its like a "REBOOT" kinda thing,) should work, or Press and select many and try and delete all off them?
Hope it helped.
-W

If you're using iOS 7:

Tap and hold a message. Select "More" when the selections pop up. Tap the messages you want to delete. Be careful, as if you only want to delete specific messages, sometimes when you're scrolling, one of them might get accidently selected. When you're finished, tap the trash icon". Tap "Delete". You're done!