The joke is: why did the hipster burn his mouth? Because he drank his coffee / ate his pizza / etc. before it was cool.
Why is it funny? Does the hipster have special meaning or background?
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Hip and hep are adjectives from American slang of the early 20th century, meaning in the know. According to the Historical Dictionary of American Slang, hip become the common form by the 1960s. The suffix -ster nominalizes an adjective, so a hipster is someone in the know, that is, someone familiar with and sophisticated about societal trends. The HDAS can find an attribution from 1940.
The HDAS traces the slang cool meaning fashionable back to 1946. Putting the words together, we can say that hipsters appreciate trends that are cool. In fact, the most avant-garde, the hippest of hipsters pride themselves on appreciating trends before other people catch on that those trends are cool.
So the joke, such as it is, is word play on the two meanings of cool -- the one meaning not elevated in temperature and the slang one meaning trendy. So in the slang meaning, a hipster tries things before those things are commonly judged to be cool. But extending that to the ordinary meaning in eating or drinking means ingesting things that are hot and liable to burn.