Sometimes I've seen the term "hyper-Calvinist" used to refer to someone who is strongly Calvinistic, or who holds to all 5 points of Calvinism, or who holds to traditional Calvinistic positions regarding election, free will, etc. But those are not technically correct uses of the term.
"Hyper-Calvinism" is a distinct theological position that states that only the elect are obligated to repent and believe, and thus unbelievers should not all be exhorted to believe in Christ or turn in repentance to God. The practical application of this for the true hyper-Calvinist is that gospel preaching to the lost or evangelistic witness are not needed.
More on what constitues true hyper-Calvinism and what distiguishes it from Calvinism is here.