The meanings of these adverbs are simple, although they are used in some special ways.
Basically, hence means “from here,” thence means “from there,” and whence means “from where”:
We shall depart hence, from here in Los Angeles tomorrow morning.
Our friends who live far away in New York will depart thence at the same time, and we hope to meet-up in Chicago.
I do not know whence this package came, so I am afraid to open it.
These meanings can also be extended to refer to time, causes, and reasons, as well as space:
The evidence is clear. Hence (from this reason), the defendant should go free.
The holiday was first celebrated in 1932, and thence (from that time) every year afterwards.
It is unclear whence (from what cause) his odd behavior originates.
Although all of these usages are great English, they do sound a little formal and old-fashioned. In fact, probably most English speakers use only hence, being less sure how to use thence and whence.