I saw a baseball catcher throw to the third baseman after each strikeout.
Is there any particular reason for this?
Is it just a custom?
The catcher throws to third to give the fielders something to do after a strikeout (in which they had nothing to do). See this article:
After a strikeout, it is common for catchers to throw the ball to third base. In any given baseball game there’s a lot of standing around in the dugout. Throwing the ball around shakes things up for the fielders and helps keep them on their toes.
Throwing the ball to third also keeps the infielders’ arms loose for throwing. The routine can even provide relief for the pitcher and give them a quick but much needed break. The catcher uses this routine throwing tactic to keep everyone on the same page in regards to the current number of outs.
Standing around can be very fatiguing, especially in the summer, but the catcher can regain players’ focus and keep players mentally sharp. It’s important every player is prepared for what is going to happen next, and it can be easy to lose train of thought when the game seems to be at a standstill.
The catcher almost only throws the ball to third base when there aren’t any runners on base.
Chicago Cubs third baseman Kris Bryant says he thinks catchers throw the ball to third after a strikeout to allow the pitcher time to walk around the mount and refocus.
The word for this is throwing "around the horn":
Around the Horn
If a strikeout occurs and no one is on base, it's common to see the catcher throw the ball to either first base or third base. This starts the team throwing the ball around the infield, which is known as "around the horn." The ball will often go to the third baseman, second baseman, shortstop, then back to the third baseman. Sometimes, the ball goes from first base to shortstop, second base and third base. Almost always when you see a team go around the horn, the third baseman gets the ball last before giving the ball back to the pitcher. This is usually done to help keep the infielders warm and ready in case the next batter hits the ball to them.