Expressions used in Everyday Spoken English in Social and Professional contexts
A mark can mean a signal. If you tell someone to begin on your mark it means you will signal them when it is time to begin. A mark can also be something that indicates a starting position at the beginning of a race so when someone says 'on your mark,' it means to put yourself in a position where you are ready to begin. If you give someone the instruction to begin or to do something on your count it means you intend to count them in or count to an agreed number before beginning.