The best way to show you some of the changes is with an example. Because we havent really seen anything from the Necron dynasties yet, were going to look at the Annihilation Barge, staple fire-support gun platform of the undying legions:
So this thing looks VERY different in the new Warhammer 40,000.
For a start, its using the same stats as everyone else, so armour values on the various facings are out, and instead, we have Toughness, Wounds and an Armour Save, making it more comparable in durability to other large monsters and massive beasts of the Warhammer 40,000 universe.
Also, its got Attacks and Strength! So it can fight (albeit inexpertly) in combat. This represents it literally ramming or smashing into enemy units.
Some dedicated combat vehicles (commonly what used to be Walkers), will have melee weapons too, like the classic Dreadnought power fist, but most vehicles will need to make do with crushing enemies under tracks or crumpling them beneath anti-gravitic engines. Generally, these attacks will have a poor to hit roll (5+ or 6+) but high strength because if a Land Raider runs you over, youll feel it. There are exceptions of course Ork vehicles can be kitted out with some pretty deadly close combat options, which now function just like any other specialist close combat weapon: get hit by a Deathroller, for example, and prepare to be a pancake.
Vehicles will be affected by all the other new rules weve talked about too, so they will be able to move as any other model would, including advancing. They shoot just like everyone else does, including (with a few exceptions) -1 to hit with heavy weapons if they move. They can even charge! which effectively replaces the Tank Shock rules, except ANY vehicle can do it and they then fight just like any other unit in the Fight phase.
Generally, youll find that vehicles still fill the same roles in your army as they always have, but without so many exceptions to the core rules of the game. Youll find them to be very durable, probably more so than they are today, and best used in coordination with infantry and where their own specialisations can be used to full effect.