The stonks meme is made to poke fun at some aspects of the stock market. It’s likely that the stock market is meant to be very serious, and that this meme was created to express a different point of view. In some instances, the people who use the meme are said to be purporting the implication that people who obsess over the stock market are nerds or somewhat lame. In other cases, people use it to just poke fun in good spirits as Wall Street-type personalities.
As for why it's called "stonks" rather than the correct spelling of "stocks", this follows the meme trend of misspelling things. Some refer such phenomenon as "dank memes", where the spellings of the meme name or some words are intentionally misspelled for the sake of humor.