A letterman is a varsity high school student athlete whose participation in games is frequent and beneficial to the team. Varsity players can come from 10th, 11th and 12th grades, usually. On rare occasion, a 9th grader can be on a varsity team. Very seldom anyone younger and some states have laws that govern how old the kids have to be before they can be part of the varsity team.
For example, my younger son was a baseball player. While he was a starting catcher on the baseball team from the time he was in 7th grade, he could not be on the varsity team until 10th grade. So, no letter for him until 10th grade. By Georgia state law, no one younger than 9th grade can participate in varsity baseball, or any other sport. They can play on school sponsored teams, but it has to be on a junior varsity team.
My older son was a swimmer. The high school he attended had a swim team and he was made part of the varsity team in 9th grade (first year of US high school) because he was fast. In fact, some of his buddies would sneak him into high school swim meets when he was in 7th and 8th grades so he could get points for the team. They never caught them at it, but someone eventually blew the whistle on the scheme (see above state mandate), so they had to stop. He had a letter as a 9th grader.
All this brings us back to the jackets. Traditionally, athletes who could afford them bought woolen jackets in the colors of their school. These jackets would have leather or vinyl sleeves. Athletes would sew their letters onto the fronts. Sometimes schools would/will provide jackets for 11th and 12th graders so they could sport their letters and mom and/or dad don't have to buy them.
Here's an example of the jackets. They can come in any color you can think of for the body, but the sleeves are usually white or lighter in color.
Hope that helps.