http://en.wikipedia.org/wiki/LTI_system_theory... Linear Time Invariant systems are the simplest category to study. The right-hand side (the generator of the dynamics) only depend on state and input but not time, hence they're time invariant.
Whether the systems are defined on continuous time (ODEs) or discrete time (difference equations) - but typically continuous state- they are amenable to Laplace or z transform methods, in other words can turn dynamical systems into algebraic equations.
time invariant systems also include nonlinear systems, which cannot be treated as LTIs unless linearized or through special methods.
Up the complexity ladder are systems where time enters into the right hand side periodically.
If time enters the equations arbitrarily, then the system can be truly complex.
As Rene' says, SISO are just in contrast to MIMO (Google: MIMO antenna). This concept is independent of time-invariance. SISO are scalar i/o systems, while MIMO systems are vector i/o.