A curtsy is an old-fashioned half-bow that shows extreme respect. A woman or girl is generally expected to curtsy when meeting the Queen of England.
There aren't many opportunities these days to curtsy, stepping forward with one foot, slightly bending both knees, and lowering your head. You're much more likely to read a reference to a curtsy in an old book or observe an actor curtsy on a stage than to see people curtsy in real life. The word curtsy sounds a little bit like courtesy, and that's exactly where it comes from.