Solipsism is a philosophy that the only thing that you can be sure exists is your own mind, because you experience it. Everything else, like other people, the world, and even your own physical body, may be an elaborate fraud that you dreamed up because you got bored. You cannot be sure that other people aren't philosophical zombies, you cannot be sure that other people even exist. Even the world and your body may be a dream. It comes from the latin solo ipse, meaning, "Only Self."
Solipsism is non-falsifiable. Anything I could demonstrate to show you that I'm conscious could be dismissed, as you don't directly experience my mind. In fact, anything I point your attention to could very well be imagined on your part. That rock I dropped on your foot? It's possible that neither the rock nor your foot really existed in the first place. The pain you feel may just be leftover guilt from something you forgot. Or remember.
Since it's non-falsifiable, and leads to some very bizarre conclusions, most philosophers reject solipsism. Even if it was true, you could draw no useful conclusions from it. If you're really a brain in a jar, imagining that you're reading this post...well, could you stop? Recreate the world to suit your own needs? Escape from what seems to be danger? Since you don't seem to be able to stop, you may as well assume it's real.
One of my favorite quotes says: "Reality is that which doesn't go away when we ignore it." Solipsism amounts to plugging our ears and asserting that we can anyway.