Most submissions are chosen with a weighted random draw. The longer you wait without being picked, the better your chance becomes.
During a stream: your selection chance grows while your submission is waiting.
If you sign in with Twitch: if none of your submissions from the random draw are picked, your saved chance carries over to the next stream you submit to. It can keep building from stream to stream until you are selected.
If you submit more than once: your submissions share one selection chance tied to your Twitch account, so submitting twice does not double your odds. If your account is drawn, one of your waiting submissions is chosen.
If you are a Twitch subscriber: you get one guaranteed submission per stream. You can also have submissions in the random draw.
Your guaranteed subscriber pick does not use up your saved chance: getting your guaranteed submission shown will not reset the chance you have built up. Your saved chance resets only when one of your submissions is selected through the random draw.
Sign in with Twitch before submitting if you want the site to remember your selection chance between streams. You do not need to be a subscriber.