
It is a light wargame for 2 players (expandable in multiples of 2 typically) about WW2 ground combat. In videogame terms this is kinda like Call of Duty instead of ARMA. It is fast paced (you can easily get three games in in a night), realism is dropped in favor for faster gameplay, and you have toy soldiers instead of chits. There are no advance rules like engines blowing out of tanks, infantry fatigue, or supply lines. You just have card driven movement and dice result combat. The game is deep, just not complex, and there are more missions than you will ever play (something like 55 official missions).
The game is played on a simple board of 9x13 4inch hexes:

Each hex can have a modifier hex put on top of it to change the battlefield. So the field quickly gains a forest, cities, hedge rows, or a river:

So in ten minutes you can go from picking a mission to starting. Comparing that to something like Advance Squad Leader or Flames of War, which take about an hour each, and you could have played the game and be putting it back up before they even start.
If you have a keen eye you will see three red lines on the board, breaking it down to sections. These are the flanks you play the game in. Gameplay is done on a I Go You Go (IGYGO) basis. On your turn you play one of your five command cards. A command card tells you which sections and how many units you can move that turn:

So if you play Probe left flank, you get to move two units on the left flank. They can leave the left flank, and shoot at units outside of that flank, but they must start there. Pretty easy right? Combat is done with special dice:

Which are pretty self-explanatory – shooting at tanks, roll a tank or a grenade to blow them up. The flag is a force retreat. Every unit has different move and shoot ranges, incover and out, etc.
Without getting into too much about the rules, it plays very well. It is an excellent “arcadey” version of WW2. Best of all is that the game has been expanded a lot:

So you are not stuck playing Western front, Americans/English vs Germany. Want to play Eastern front, great there is a Russian army with Commisar rules. How about Pacific? There is Japanese. Mediterranean theater, grab those Italians (who have missions against the Allies and the Axis). There is an airpack to add air power, and you can daisy chain multiple sets to make Omaha beach or just one gigantic battlefield. There are even third party maps pre printed with the terrain tiles so setup is even faster:

Why do I enjoy it so much? To me Memoir 44 is like Avalon Hills Dune, it is a system polished so well that it is damn near perfection. The game “engine” for lack of a better word has been expanded on numerous times since. The original game, Battle Cry, is currently in print and is Memoir in the American Civil War (the current release has the updated Memoir rules). But there is a version for most eras of combat:
Command and Colors Ancients
Command and Colors Napoleonics
Samurai Battles – Feudal Japan
The Great War – WW1
Battlelore 1st&2nd editions (released by two different companies) – Fantasy
Having played all but The Great War, the one I always come back to is Memoir. It has the most support, official and fan, it plays very well, and my wife and I get four games in in a night easily (2 missions, one time each playing each side).
The version on steam is a pay per game system and so not worth it - despite me spending alot of money on it when it was on the DOW website.
All pictures are from BGG or GameDad