If you're familiar with Dominions 3, think Dominions 3. It's basically a slightly modified and vastly more content-filled version of MoM.
If you don't know Dom (and you should, it's fantastic), think Civilization instead:
MoM starts you off with a city. The city has a few core characteristics, based on the terrain under its zone of control. Different structures can be built in the city, to modify its core characteristics and to allow the city to produce more buildings and various units. How well a city can exploit its characteristics, and how many it consumes, depends primarily on its population level (and what race the population is), and secondarily on what it has built.
As the game progresses you'll send out settlers to found additional cities, and armies to conquer foreign cities. The latter is how you gain cities with populations of races other than the one you started the game playing as.
Basically, it's just like Civilization. The 2 big differences are research and warfare.
Instead of chewing your way through a shared tech tree, MoM has a pile of much smaller tech trees, and just who can access them is very fluid.
Magic tech - the civilisation advancing techs - consists of a number of spells, each of which requires a certain amount of spell books in one or more spheres of magic to unlock. How many spheres a faction can access and how many books it has in each, is decided during match setup. The result is that different factions end up being able to research very different parts of one magic tech tree.
Construction tech - Building construction in cities - is pretty much the same for everyone, regardless of circumstances. But due to racial modifiers, different races can unlock certain combinations of buildings faster than others, and have an easier time supporting certain combinations of buildings.
Unit tech - the caveman to carrier stuff - is probably 75% race-specific. There's some basic unit types shared by all, but pretty much every type of combat unit can only be built by 1 race.
Like in earlier Civs, units move around the maps in stacks. But combat isn't stack vs. stack as in the earlier civs. Instead combat brings up a tactical map where you and your opponent move around your regiments, throw spells and fuck with each other. I guess that does sound almost exactly like HoMM, but it really isn't. Individual units in MoM are individual units, not stacks within a larger stack. MoM's tactical combat plays far more like a traditional wargame than HoMM. And despite the individual units being somewhat simpler than HoMM's, the combat as a whole is a fair bit more complex.
Finally, like in Call To Power, Age of Wonders and more recently Warlock, MoM is played across more than one dimension (2.. so not a lot more, but still), and neither one is just sitting there, waiting to get gobbled up. There's neutral factions running around, and a host of different sites that can fuck with you, and if subdued, provide significant advantages.
Probably the games that has most in common with MoM and which have actually been released at this time, are the Dominions games from Illwinter. The big fat difference between Dom & MoM (apart from amount of content), is that Dom has a province-based strategic map, while MoM has a borderless, tile-based one.
