there are several important reasons for breathing correctly, and a few times when you don't exhale until the rep is completed (more on this...)
normally, you inhale during the eccentric contraction...the 'easy' part...lowering the bar on bench press for example.
then, depending on the lift, you will start to exhale at some point of the concentric contraction...the hard part....pushing the bar back up in the bench press.
now, this is all assuming you are NOT powerlifting. powerlifters (I believe) DO hold their breath. The reason is to stabilize the torso via internal pressure built up via breathing in.For the same reason, when lifting heavy, you usually won't begin to exhale until about 50-60% of the way through the concentric movement...past the usual sticking points.
Also for this same reason, you don't exhale until the rep is at least 90% completed when squatting, ditto for deadlifts. The internal pressure helps stabilize the abs, which in turn help stabilize the lower back, which is vital when lowering injury potential on those lifts.
It should feel natural to breath in on the easy phase, and out during the hard phase.
Haven't you ever heard the guys who grunt at the gym? (like me) I'm not talking about obnoxious guys, but the real hardcore guys that are pushing their limits, going for that last rep?
well, you can't grunt unless you are exhaling, and you are exhaling because you're curling that 100lb dumbbell up and its hard as hell.