The masses relate to it because it offers hope. Who needs hope? - the hopeless. See also "Shawshank Redemption" for a similar, simple story.

This movie, like all movies, is a fantasy: in this case, a fantasy for lazy, simple (minded) people who fantasize about fame & celebrity (Forrest is on TV and in the newspapers multiple times, meets presidents and inspires celebrities, etc.) and money ("fate" sees to it that his shrimp business makes him a millionaire and emphasis is put on how even his most mundane musings end up making people millionaires) without actually doing any work or coming up with any ideas to deserve either.

Life happens to Forrest, and these luckless layabouts relate to Forrest. Unfortunately for them, life is not like a box of chocolates where you don't know what you're gonna get, rather, it's based on natural selection where doers earn the good chocolates and people like their hero Forrest usually end up with nothing at all. Forrest Gump is a poor role model and this is an average movie.