This can be in terms of graphics, gameplay, general quality, whatever.

Which games do you think were the biggest leaps forward over their immediate predecessor, and why?

Aside from the jump from 2D to 3D?

Well 3D World is technically the immediate predecessor of Odyssey, and I'm sorry, but it's no contest, Odyssey crushes 3D World. There's certainly a time and place for 3D World and it's not a bad game, but to go from that to Odyssey, damn. Same with Triforce Heroes being the technical predecessor of Breath of the Wild. I don't actually hate Triforce Heroes, but it's at the bottom of the heap of Zelda games, while Breath of the Wild is near the top. Super Mario Party is another big jump from any recent predecessor, best since the Gamecube era at least, getting a series long since gone astray back on track.

I'd like to also nominate Portal 2 over Portal.

Final Fantasy 4 - Huge immersive story and fleshed out characters far beyond what Final Fantasy had before.
Final Fantasy 7 - Gigantic game compared to FF6.  Lots of content.  The pinacle of video game story telling IMO.  Also the FMV graphics were very impressive in their day.

Breath of the Wild - It's 3D Zelda with the huge open world feel of the old 2D Zeldas.  Really huge and highly polished world with unparalleled freedom.
Hyrule Warriors - Just putting Dynasty Warriors in Hyrule makes the game so much better.
Mario + Rabbids - I could never get into X-Com, but I enjoyed the hell out of Mario + Rabbids.  The world and characters are a lot more interesting.

Puyo Puyo Tetris - I wasn't really a Tetris fan until I played this version.  It takes the game to a whole new level.

Assassin's Creed 2 - I felt the first game was shipped incomplete, but it had potential.  The second game fully realized that potential.

Dark Souls - I really thought Demon Souls was great back in the day, but I went back and played it after playing Dark Souls and it just feels bland by comparison.  Dark Souls has this huge varied world to navigate and conquer and it is continuous instead of always returning to a hub world.

Civilization Revolution - All the fun of a Civilization game but streamlined so you can finish a game in a couple of hours.

Wii Sports Resort - This is so many more games and much better control than Wii Sports
Mario Kart Wii - To me Mario Kart really came into its own when it gained motion controls.

Guitar Hero 1 and Rock Band 1 - This series actually started out with the games Frequency and Amplitude, neither of which used plastic instruments.  That is why Guitar Hero was a huge leap.  I didn't come in to this series until GH3, but it should be obvious how much a leap it was to have plastic instruments.  Then Rock Band came along and took this genre to the next level by having a whole band of plastic instruments.  (GH and Rockband have different publishers, but both games were originally designed by Harmonix.)

Nes Super mario bros 2 (Japanese) t Super Mario Bros 3 was a incredible jump in all level (Game play,graphics,etc)

Super metroid to Metroid prime was shocking and the first time i really feel what was to be alone in a alien planet. one of my favorite games of all times.

That is what i can think for now.

Sorry for my bad english.

Elite Dangerous. It's been a while since the previous one (1995) so after a 20 year break graphics are obviously a little bit improved. The most amazing thing is the accurate (as far as we know it) representation of the entire milky way galaxy.

Heh, I was about to go sleep when I realized I had missed the most obvious game of all:

Super Mario Bros - The predecessor to this game was Mario Bros.  You know, plain jane, hit the turtle/crab/firefly from underneath Mario Bros.  It was just one board at a time with no scrolling.  Then SMB came along with 32 side scrolling stages, that took you through this trippy, magical fantasy world.  You could get permanent power ups.  No game ever did that before.  It had permanent music, very catchy.  No game had done that before either.  It has secrets everywhere including warp zones where you could skip tons of stages at a time.  Super Mario Bros wasn't just a huge revolutionary leap over Mario Bros, but it really was a huge revolutionary leap over every video game that had come before it.  The biggest leap in all of gaming came from Jumpman himself.

Honorable mention goes to Super Mario Bros 3.  Somehow they took the most popular game ever made and then made it a thousand times better.  SMB3 is an amazing game, but as far as "most improved" goes, the hands down winner is the first Super Mario game.

The leap from Mega Man 8 -> Mega Man 9

The 12 year wait between sequels was totally worth it just for MM9's amazing grafix alone!

God of War 2018

Grand Theft Auto 3. I think it's the runaway winner here.

Grand Theft Auto: San Andreas

Holy shit, Rockstar really went above and beyond after Vice City (which was stellar by itself). Increased the size of the map by like five times to include 3 full unique cities, and some countryside, too. Many improvements like being able to swim, climb, rotating the camera while in gameplay, etc. Way more stuff to do in general (like getting aa fricking JETPACK). 

And it all fit on a PS2 disc, somehow, someway. GOAT game.

Wii Sports Resort

Wii Sports I really liked, but Resorts use of the Wii Motion Plus just made it infinitely better. Plus just more sports, more content in general.