Both words mean "to study" or "to learn". Whereas 學習 can be used both transitively and intransitively, 學 is normally reserved for transitive use.
e.g. 我學(習)漢語﹐她學(習)法語。
I study Chinese, she studies French.
我學習﹐我弟弟不學習。
I study, my younger brother doesn't study.
In the second sentence, the word 習 cannot be omitted.