What does it mean when people (e.g.americans) say --th grade?

[Steve A]

The first year of school in the US is called kindergarten. The children usually start when they're 5 years old.
Then comes 1st grade, which is 6 year olds.

Different US states have different rules about starting. It usually involves the child's birthday. It could be that the child has to be 5 by July 1 to start kindergarten that year. Some parents hold their child back for a year so they'll be more mature.

In high school, the first year is 9th grade or freshman, then 10th grade sophomore, 11th grade junior, 12th grade senior. The four years of college use those terms again. Some have started to say first years instead of freshmen to not be sexist.