Spontaneous processes are those processes which can take place on their own under given set of conditions. Non-spontaneous reactions are those which do not occur on their own under the given set of conditions.
In thermodynamic, for spontaneous processes, the change in Gibb's free energy is negative. That is for spontaneous processes
ΔG0 < 0
For non-spontaneous processes, the change in Gibb's free energy is positive. That is for non-spontaneous processes
ΔG0 > 0