It's quite straightforward, really, I guess it's my dodgy explanation.
E.g.
You want to fly a SID with various 'at or below' constraints along various waypoints. Your initial clearance is to climb to FL120, whilst respecting the constraints.
You set FL120 in the FCU window, and CLB mode will engage automatically at acceleration altitude.
In Climb mode, the aircraft will level off at all of the preprogrammed constraints in the SID. It will then climb again to the next constraint, and the next, all the way up to FL120 which is what is set in the FCU window.
If at any point you are recleared 'unrestricted' up to FL200, you turn the FCU knob to FL200 and pull it. Open Climb will ignore all constraints in the FMGC and climb you up to FL200.
Exactly the same principle applies in the descent!