Rhythm can mean several different things. The most common is used while fighting/sparring. The great Karate Champion Joe Lewis (deceased) came up with what he called set point fighting. It used the opponents rhythm against him. It involves being aware of when he is about to move. by watching his movements you can usually predict exactly when he will have one of his feet halfway to where he is going to move it. If you know that and are in range to strike without having to move into range, you can attack so that your attack hits while he is in mid-step. Using that theory Joe Lewis won many competitions. I learned this back in the 1970's. I used it to play with my opponents mind. They could not figure out how I was able to nail them so often and them not be able to stop it.

Hope this helps...

...

That word has a couple of different meanings depending on what context it is used in. Usually it refers to your movement and activity in relation to how aggressive you are. You sometimes also hear about "timing" a fighter and that's when his opponent is intending to catch him doing something based on his rhythm and movement for the purpose of nailing him and has a specific shot in mind for doing this. That of course becomes easier if the first fighter basically fights for too long the same way, at the same pace, doing pretty much the same things. To prevent this he should instead vary his pace, movement, and aggressiveness at times making it harder for his opponent to time and catch him coming in or in the middle of doing or throwing things.

An old trick that I teach fighters and would sometimes use myself was I would sometimes slow my motion and movement down just a little and take the level of aggressiveness down a few notches. Then I would look for my opponent to unconsciously to do the same. Inexperienced fighters will and sometimes semi experienced fighters even will because they think they have a brief opportunity to rest and conserve energy for later rounds. If they do this then I would quickly explode at some critical point when I saw a good opening, throwing with speed and power and become aggressive, trying to catch him in a semi-relaxed state.

Rhythm also refers to how smoothly and easily you coordinate what you do with your hands and feet in relation to your movement. Positioning yourself in relation to your opponent and being able to do that better than he can in relation to you as well as control that can dictate a fight in a lot of ways. Fighters who have poor rhythm struggle with the above and usually end up following their opponents around the ring or cage and are often not in positions of advantage over their opponent very much or very often then and their effectiveness becomes stymied.

What does rhythm mean in dance, it means the same in sparing. You should use at least 3 rhythms to help remain unpredictable.

The individual's center of gravity must be balanced. Most martial artists charge forward, punch/kick and lose their balance. When the opponent punches, you block/evade and then attack. Or do both at once. You don't move back (losing your balance). If a combatant is focused then he/she/it won't lose balance.

it means confusion. Maybe rhythm belongs in tai chi or some kind of "non combative" martial arts.

The fluidity and consistency of your strikes