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A degenerate (in its derogatory use) is a person who, from the perspective of the speaker, is "less than" or has "fallen from grace" — i.e., has degenerated from some pure or true form, into what they are now. In the US, the term has often been applied by the "rich, white, morally correct" folks to such unwanted groups as hippies, homosexuals, drunks and dope fiends.
The term was also frequently used by explorers, missionaries, and "scholars" from the so-called "Old world", to describe the so-called primitive inhabitants of the Americas and Africa. The term stuck with such people long after they were part of the world's "modern society" when trying to make a case that some races were inferior to others. This is why most people imagine a toff voice in their head when they think of the word.
Renewed usage: neo-Nazi and neo-reaction
The term "Degeneracy" has come back into favor among the worst people the Internet has to offer. In context, it tends to be used to refer to people who are either not white or white but not racist (very much like the word "cuckservative"). 4chan's/8chan's /pol/ is particularly fond of using the word in a "ha ha only serious" kind of way.
On the internet, "Degenerate" can be used, and is often used interchangeably with the words "Cringeworthy", "Cancerous" (As a slur) and "Autistic" (Also as a slur) by Internet tough guys and people within right-wing circles other than the alt-right who may use the terminology to refer to people who have very unconventional sexualities, are paraphilic (Voraphiles for example), have nonconformist beliefs or to describe people who are extremely eccentric or weird. It can also be used to describe content such as pornographic material that someone may find disgusting as "Degenerate".
Its usage in this context differs only barely from how the neo-Nazis and WW2 Nazis use the term, however, the word is used more commonly to mock or target someone who is still deemed too unconventional for Conservatives and edgelords alike with the sole purpose to make that someone feel inferior since those Conservatives and edgelords don't tend to hate Judaism, people of color and those who are physically disabled, unlike the Nazis.
In medical context
The word degenerate (Or the more often used adverb "degenerative") is used to describe diseases that worsen the living conditions of the person affected, the disease is rarely caused by an external bacteria or virus, but rather it is caused by the body of the person affected.
An example is a disease caused by getting older, as you get older your spine will start hurting because of the spinal disks.