Yes, condoms can break. That's why they say on the box that no method is 100% effective.
It can happen because of friction, i.E. That there's not enough lubrication and it causes a tear. It can also happen if there's not enough room left in the tip, and the force of the ejaculation can cause it to pop.
Try trojan. They're a pretty good brand that we haven't had any problems with.