Yield curve control is a way that a central bank (like the Federal Reserve in the US) uses to influence how much people have to pay to borrow money. When a central bank controls the yield curve, it sets a target interest rate for borrowing money, and it actively works to keep that rate at that target.
If the central bank sets the target interest rate low, it wants to encourage people to borrow money, which can help grow the economy. The central bank might do this when the economy isn't doing very well.
If the central bank sets the target interest rate high, it wants to discourage people from borrowing money, which can help prevent the economy from getting too hot and leading to inflation. The central bank might do this when the economy is getting too strong.