The game is called “spider” solitaire due to the relation of spiders having 8 legs, and the 8 foundation piles that need to be completed in order to win the game. While the current version originates from 1949, the first mention of spider comes Games Digest published in 1937. They describe the game we know today as Spider, but it slightly differs with the tableau having 50 cards instead of 54. However, they talk about it as a well-known game, so it's likely Spider has its origins from the early 1930's at the very least.
Spider Solitaire later grew in popularity with its inclusion in Microsoft Windows in 1998.