Benjamin Franklin said this famous line at the time of the signing of the Declaration of Independence in July 1776. The meaning of the quote was that the signers of the Declaration, as well as colonists in general, had to help each other and support each other or they were doomed.
The line is, of course, a pun. Franklin is using the figure of speech "hang together" to mean "stick together" or "support one another." He puns that with the phrase "hang separately." By this, he means being executed by hanging.
So he is saying that if they do not support each other, they will be executed. By extension, he is saying that if they colonies as a whole do not support one another they will all be defeated by England.