Its based on the old Panzer General game.
Basically its a turn based war simulation game where you control the German/Axis forces. You get a certain amount of credits which you can use to buy your core force. This force follows you from battle to battle and is often supplemented by non-core forces in each battle. The basic types of forces are infantry, artillery, field guns, scout vehicles, tanks, anti aircraft, fighters, strategic bombers and tactical bombers. For some missions you also get access to fortifications (pill boxes and fixed artillery) and ships, but these are battle specific and don't follow you. There is no base building and the focus is entirely on maintaining your core force.
Whilst the name of the game seems to suggest the focus is on tanks, its much more a combined warfare type game. There is also a rock/scissors/paper type thing, although its quite blurred and really depends on the specific type of unit and how much experience they have (for example, basic infantry will get mowed down by tanks in the open, but grenadier troops will do a bit better).
There is an experience points based system whereby your units gain experience in combat. This passively allows you to increase their abilities and if they gain enough experience you can use credits to overstrength them. You gain credits by capturing cities, but get very few credits passively (and they actually removed passive credits from the expansion packs) so the focus is very much on attacking. You can also reinforce your troops when they take casualties, either with "green" which are really cheap, but will result in the units experience dropping significantly, or with "experienced" troops which will result in the units experience staying the same, but which cost a lot more.
The missions mostly involve capturing certain specified objectives (usually a few cities or airfields) within a time limit (usually between 20 and 30 turs). If you can capture the objectives within a certain specified time you are granted a decisive victory. This gives you more credits for buying/ugrading troops for the next battle and sometimes lets you leapfrog battles or participate in non-historic battles. Its generally pretty hard to get a decisive victory on the first play of any battle.
The game is fairly accurate historically (especially the add-on packs) although the main game itself can see you invading the US if you get enough decisive victories. The availability of new units is historically accurate too.
Its mostly a single player game, although there is a play by mail function that i never tried.
The main game itself is a bit expensive IMO, although the expansions are dirt cheap at about 4 euro each (note that there is no voiceover in the expansions, but that is just fluff anyway and doesn't effect the actual game). The main game takes you through the course of the war (around 32 battles), whilst the expansions focus on particular years in much more detail. So for example in the main game you might fight around 5 battles from 1939, but in the add on you fight around 20 battles from this period. The expansions are also much more historically accurate which will please war history buffs.
Any questions about the game, just ask or check out the matrix or slytherine websites.