ODE45 is a Runge-Kutta single step solver using the pair of order 4 and 5 solvers as communicated by Dormand and Prince. The parameters for the order 4 and 5 are chosen such, that the a minimum number of function evaluations is required.
The local discretization error is measured by the difference between the order 4 and 5 solutions. The time steps are chosen such, that this difference is smaller than the given relative and absolute tolerances.
You can find all details by reading the code of ODE45, especially the references will be helpful.
