Time complexity is a measure of how long a computation takes to execute.
For a Turing machine, this could be measured as the number of moves required to perform a computation. For a digital computer, it could be measured as the number of machine cycles required for the computation. Space complexity is a measure of how much storage is required for a computation. Both of these measures are functions of a single input parameter, the size of the input. Again, this can be defined in terms of squares or bytes.