It seems there is some debate over the title of this series. My copy of the "Millenium Edition" and the original have it spelled Heroes of Might and Magic
The Heroes of Might and Magic series is an interesting entry into the strategy game category. Like Civilization it is a city based strategy game. You control one or more cities which produce your army, magic resources and special bonuses. The cities are controlled from a seperate screen much like Civilization. Resources are located on the map in the form of mines which can be controlled, or deposits which can be taken once. Armies take the form of a collection of different types of troops led by a Hero. On the main map only the hero appears. When an encounter occurs the game switches to a tactical screen. This screen is much like the encounter screens for later Ultima games. Units start out to the left or right of the screen and move across it to fight each other. Though simple, this tactical screen does offer a lot of options that can greatly effect the outcome of the battle.
A major difference from Civilization, besides the units being grouped together, is that a Hero can move a considerable distance on each turn. Leaving a city undefended can be very dangerous because an enemy Hero can run right past one of your heroes and take the castle in only a couple of turns. This also leads to having to hunt down enemy Heroes as they run through your countryside taking over your resources if you're not careful.
Especially in the later games there is considerable emphasis on the Heroes. In a battle the Hero does no fighting, but their influence and magic abilities effect it greatly. Heroes have XP and levels, and increase their attack, defense and magic abilities. Their attack and defense abilities are added to their creatures, and the magic spells are varied and can be very dangerous. You can also find and trade artifacts between heroes which increase their abilities.
Overall the game is pretty simple and has a low learning curve. Most of the complexity comes from the number of different types of troops, artifacts and spells. You can play single scenarios, a campaign (a few connected scenarios) or multiplayer. I'd say it has a pretty high addiction factor and is definitely an extreme time waster.
All three games were created by the same person who did the Might and Magic series, Jon Van Caneghem. In his Intro for the Millenium Edition he mentiones that HMM was originally a sequal to his game King's Bounty, but turned out completely different.
The above WU details the changes in HMM2 and HMM3. They basically fit in the "more of the same" category, which, in this case, isn't necesarily a bad thing. If you've never played Heroes of Might and Magic before you should try and get ahold of a copy of HMM3, which you should be able to find right now for about $10 USD.