Removing or reducing limitations.

For example draw distance use to be horrendous in games, go play Driver on PS1 to see what I mean. Slowly able to show more characters, more detailed models and textures and big one that gets ignored, reduced load times.

I never said they delivered on those promises, just that it's something that I want to see.  I want to see bigger scale games that just couldn't be done before.   I know that we aren't going to get any huge leaps like from 2D to 3D, but just something that feels larger scale than previous generations.  And products that work on launch rather than stuck in a broken state and patched later on.

graphics

it means nothing, it's a marketing term anybody who likes to actually play games won't bother too much with.

This generation feels like the jump from the 8-bit to the 16-bit era. Graphics got better and games were just mechanically superior but most of them were still side scrollers.

Graphical fidelity improved greatly but the artistic design didn't change much so far this generation. You can have a 60 fps game criticized for not having a high graphical fidelity, and another game trashed for having a high graphical fidelity with 30 fps. We had cinematic games last gen, now they're more graphically superior but only got subtley better in the design department (8-bit vs 16-bit style) but people still grind them.

Next gen usually just mean the next console one of the major manufacturers announce. I always hope it also brings something, something we haven't experienced before, but I often get dissapointed. Graphics used to be my measure but it feels so irrelevant although it is fun with beautiful games :).

Completly untrue.

Next Gen is just a way to say, "We have better hardware, but it will only be utilized by a small percentage of developers. For the most part it will feel like last gen. Or pre-last gen."

Better graphics, larger, more immersive worlds

If you believe that than expand upon it.

Little has changed in the way most games play. Biggest transition was probably 3D from 2D, but that was still 20 years ago. 

Not much has changed in fps from doom and wolfenstein, they are still fundamentally the same. Word adventure rpgs are nearly extinct, like very early DnD.