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If EITHER of you should press the infamous "next" button, the chat session will end, and another random connection with another completely different random stranger will ensue.
So, what this means for you is if you are particularly uninteresting or uninviting on the eyes, you may get "next"-ed over and over, such that you may find the service to be somewhat depressing.
Then, you are connected completely at random to the first available person who has done the same thing.
Once you are connected you may have a chatting session with this unknown stranger, but at any time during the connection both you and the other user have the option of pressing "next".
In any event, I think by now you've seen what makes us such an attractive Chat Roulette similar site, and if you're a newbie to random chatting, I think I've given you enough to go on to get started.