Questions about example sentences with, and the definition and usage of "Placekicker"

Q: What does the placekicker do exactly? I mean, the definition says that the placekicker is responsible for kicking duties of field goals and extra points. Are you even allowed to kick the ball in gridiron football? I always see players running around with it in their hands and throwing it to other players. Tho I've never actually watched a full game, nor am I familiar with the rules of the game. So is the placekicker the one who actually scores goals or something? I'm watching this TV show called Fuller House, and one of the sons of one of the main characters gets home from a game, and the younger bro goes, "How was football recital?" , and he says " It's a sport,not dance class." The mom then says, "Well, from the look of ur spotless tights, seems like dance class", to which the older son replies with "I'm the placekicker. I never get dirty."
So, if the placekicker never gets dirty, then I assume he does little to nothing and is not as productive as the other players.
Apparently the placekicker is also the team's kick-off specialist and is responsible for sending the ball into the kick-off. What does it mean to kick the ball into the kick-off?