In the computing community, hack can either mean to cobble together a solution to a computing problem, or it can describe someone who's an expert in computer security.
To the uninitiated, however (which is practically all of us) to hack a computer is to break through its security systems in order to cause problems.
(A computer security expert would like us to call these people crackers. But of course we don't.)
As for the activist part of the word, everything depends on what the activist is trying to do. His (or her) main motive might be to allow freedom of expression, in which case he won't, logically, be inserting computer code that will result in a computing system shutting itself down (that is, making a Denial Of Service attack).
(Not that logic doesn't always come into it.)
A hacktivist might have, in any case, a less philanthropic agenda. He may want to spread a message of hatred; he might want to close down government department; he might want to tell the world a few choice state secrets.
The thing is, it's hard to be seen as a goodie when you wear a black hat.
And to most of us both halves of the word hacktivist look pretty close to charcoal.
Word Not To Use Today: hacktivist. The Old English form of the word hack was haccian. The word activist comes from the Latin actus, a doing or performance.