Each physical attack adds a combo count to a character that is hit (up to 1 combo per turn). When the combo count hits 3, a stun goes into effect. The combo count on any character that is not physically hit in any given round resets to 0.
The combo count does not increase on multiple physical hits per round. So, if 2 of your characters hit the same enemy character in the same turn, that enemy character's combo count only increases by 1.
There are strategies for dealing with stuns and reducing combo counts, see the stun article about more details.
Don't confused combo count with combo rate.