Mods beat me to it.
Anyway...
DI is holding a direction on the analogue stick at the moment of impact to slightly alter the angle you're launched at.
Say you get BThrown by Ness near the left edge (for illustrative purposes ofc) at KO percent. If you don't DI, you're gonna get KOd. However, if you hold up while while you get thrown, instead of going at a ~40° angle, you'll be launched at something like a 45-50° angle, towards the top-left corner of the blastlines, meaning you have a better chance of surviving. DI won't work if you input the direction you want to "bend" your trajectory to once you've been launched.
SDI is inputting a direction while you're in hitlag (the frames when an attack connects during which the attacker and victim are frozen; think Falcon's Knee or a smash hit of the Ore Club) to shift slightly in that direction. SDI will only work during hitlag, and it doesn't affect your launch angle, only your position. Say you get hit by Ganondorf's DAir offstage, near-ish to the wall, but far enough so that even if you DI towards the wall you won't hit it. If you SDI towards the wall during DAir's hitlag then DI towards the wall too, you have a better chance of impacting the wall so you can walltech and survive the hit.
I'd suggest checking these threads next time rather than making a new one;
http://smashboards.com/threads/mechanics-techniques-discussion.368206/
http://smashboards.com/threads/the-smash-dictionary.374538/
I hope I helped! (idk what you mean by ELI5 unfortunately)