A "checking account" is a bank account that you can freely take money out of and put money into.
Usually you don't earn much interest from a checking account. So if you keep $10,000 in the bank for a year, you'll still have something like $10,000 to $10,025 at the end of they year.
However, a "high-yield checking account" pays a higher interest rate than usual. This allows you to earn more money. Usually there's some other restriction on this type of checking account. For example, you might need to maintain a minimum balance.