Daggerfall's reputation system was horribly complicated. Each faction had subfactions and those factions and subfactions changed from region to region. Actions that helped within your faction could also hurt you with some of the subfactions within the same faction. It may have been fairly believable (for a fantasy role-playing game, anyway), but it could certainly complicate your life. Morrowind's reputation system is radically simplified. You only have two reputations to worry about: your reputation within your faction and your overall reputation.
Your reputation with your faction (which I typically call "faction rep") imposes modifiers on how peope respond to you based upon their faction associations. Members of your faction will have generally higher initial dispositions toward you and those dispositions will improve as you move up within that faction. Members of factions who are not friendly to yours will generally have lower initial dispositions toward you as you move up.
Those dispositions can be improved (or lowered) through using your "people skills": Speechcraft (Admire/Intimidate/Taunt) and Mercantile (Bribery). Remember that successful Bribery increases your Speechcraft, but whether you succeed or not depends on a check against your Mercantile.
A couple of things to keep in mind. First, your rank in one faction can increase or decrease the initial reaction of people based upon how their faction gets along with yours. It is not your reputation within that faction, but your rank that makes that modifier.
Second, your faction reputation does not decrease over time. It can decrease in a few cases if you successfully complete quests for other factions, but it does not try to zero out like it did in Daggerfall. If you have 60 points of faction rep, it can go up by completing more quests, but it won't go down on its own. This is generally beneficial because you need rank, not reputation, for disposition modifiers, and you need reputation in order to get rank. Since quests are limited in number and one-shot deals, you don't need your reputation to be slipping while you're off doing something else for a while. By the same token, once you have rank, you can't lose it. You can be expelled from your faction, but you can't be demoted.
Your overall reputation is a numeric score that determines people's initial reactions, regardless of your faction affiliations. It can never decrease and since it imposes modifiers on base reactions, it can only get better. The higher your overall reputation, the more people will like you and the better the prices you will get/pay from merchants and trainers.
You get points added to your overall reputation when you complete certain quests for the Main Quest, for your factions and for a handful of side quests. Although there are a total of 173 overall reputation points available, you are excluded from some of them because you can only belong to one Great House and cannot get the points for the quests of the other Great Houses. So your point caps are:
The available points, by questline are: