Halo is our family's favorite game (there's my bias right there).
It's an incredibly complex story line game (dozens of books/ graphic novels/ etc. are written in/expanding the Halo Universe, similar to the way that Star Wars has been). In between every level there's a several minute long story section/ mini movie.
There's technically not YET a Halo 4, I suspect your MIL is talking about Halo Reach... but here is the list of them
Halo : Combat Evolved
Halo 2
Halo 3
Halo 3 ODST
Halo Wars
Halo Reach
(Halo 4 is now being created)
Halo 1-Reach is actually a circular story, with Reach being the Prequel to Halo 1.
The basic premise in Halo is this: Heroism / Saving Humanity/ Saving all the races in all the galaxies
Good to Know: At no time, in any of the games are you actually fighting or shooting other people (unless you're playing xbox live against other players in capture the flag type games, but NOT in the storyline games). There are 2 enemies in the game. An alien race named the Covenant (a collection of several bipedal alien races) who started attacking human planets, and an alien race called the Flood (similar to the Borg, if you're familiar with Star Trek) which is a blob shaped species that consumes every sentient being it comes across. In the beginning your character (and all of humanity's forces) are fighting both the Covenant and the Flood. At a certain point in the story arc, there's political division in the Covenant and Humans ally with one faction of the Covenant in order to fight the Flood together.
In Halo1 you start off the game as the last Spartan soldier (the rest having died defending / during the attack on Reach). In a later Halo you switch back and forth between being the Spartan and being a Covenant Elite and then you join forces. In Halo ODST you're part of a human "hell jumper" team that is trying to evacuate Earth (and many of the missions are just that, getting survivors to safety). Halo Wars is the only NON first person shooter (it's a strategy game similar to Dune, or Risk). Halo Reach you're part of a Spartan team of 6.
There are several recurrent characters in the game, and as I said, a VERY large back story. In all of the stories you're both the best at what you do AND recognized for it. (AKA none of this lone wolf/loose cannon stuff, but highly decorated and admired by the military higher ups and civilian higher ups, with close personal friends. The game isn't about besting a corrupt system, or criminal element, but instead much more idealistic. All of your contacts/superiors/friends in the game are moral/ caring individuals who are ALSO the best at what they do)
The game is actually quite serious, but there are also a lot of humorous moments. A lot of games go for straight out gore, Halo doesn't. It's visually STUNNING. Beautiful worlds, gorgeous scenes, the artwork in the game is utterly amazing and for each game state of the art/ gold standard for every other game to meet.
Are you shooting/fighting? Yes. Absolutely. It's a first person shooter game with over a dozen different types of weapons (2 kinds of grenades, several kinds of 'human' rifles from pistols to sniper rifles, several kinds of alien weapons). You're mostly on foot, but also occasionally piloting or driving. The blood is mostly neon blue (since you're fighting aliens).
There's a LOT of info/film out on all the halo games that you can look at. Here's a GREAT one to start with
http://www.youtube.com/watch?v=T0_jiB2hqeQ&feature=re...