There's not much in multi-player but it's decent, I play it occasionally. You can level each of the characters available for each classes (Adept, Sentinel, Soldier, etc) to Level 20. At that point you can sometimes "respec" the stats for free if you find respec "cards" (can't remember their actual name) from the Veteran (and up) packages that you can buy with in-game credits (no transactions needed, but you can buy BioWare points if you really feel like it to accelerate the process), although what is found in those packages is random. As for the weapons and upgrades it's basic stuff, you find new guns, new upgrades, and then later on you increase the level of the upgrades you found (or the weapons), or keep finding new ones until you find everything. There's three difficulty levels, Bronze, Silver and Gold (I think the third one is Gold, not sure). There's three enemy types like in the campaign pretty much, Cerberus, Geth or Reaper troops (Cannibals, Banshees, etc). You can randomize the map selection and the enemy type, or you can impose a map and an enemy type if you wish (if you create the match that is).
The maps themselves are pretty much parts of the campaign, or perhaps it's the other way around who knows (I wouldn't be surprised if they just used some parts from the campaign's maps to set them as multi-player ones). There's two new maps however that were released recently that are unique to multi-player and are the most polished (in my opinion) of the whole bunch. One happens on the moon of Palaven but geographically located somewhere else where Shepard didn't go during the campaign (probably one of the various Turian bases on the moon of course), you can see Palaven and a very nice environment during the match in which you can see Turian fighters flying around with smoke at a distance to simulate the war that's going on as you play the match. The second unique map looks a bit more "generic" but there's a nice big vista around, very nice looking environment with a big dam at a distance with "birds" (or alien flying animals that look like birds... not sure if that map is on Earth or not).
Once you reach Level 20 as I said above you can respec the stats or you can "promote" your characters which gives points for the mini-game Galaxy at War (which is kinda pointless). But the promote function can be used as a respec anyway if you happen not to have any respec cards and you do want to change the stats, but if you promote any Level 20 characters (or classes) they are reset at Level 1 and you start the leveling process over again, but you do not lose any weapons or upgrades you found. Overall it's... decent. But it feels restrained, limited, for a multi-player mode, although it's just an extra I think, of course ME3's goal isn't to turn in a new Gears of War MP-focused game (not that it's that far from such a scenario to start with). I wouldn't buy ME3 "for" the multi-player only (or "mostly" either). If you do plan to play the campaign, sure why not. If not... I would wait until you can buy it for a cheaper price than full price (I wouldn't pay more than maybe $20 if you want to only play the multi-player, but that's just me).
I'd give a solid score of say... maybe 6.5/10 to the multi-player, it's nothing bad really it can burn some time. It does seem fun at first but warning that it gets repetitive very fast, Mass Effect is just "not made" for that kind of game-play in my opinion. It's a nice addition by itself but they could have taken the MP team and the time they worked on it to help the campaign team instead for more content during the campaign.