Indeed. It affects the ability to make relations with people. Mostly in the vassal and order joining agreements of relations. -150 is the limit where vassal and order agreements can't be sent or received.

The fastest way to gain reputation is to donate gold in temple.
Build it up to 5 level and donate gold.
1 gold = 1 reputation point. (5 lvl temple)

You can also donate resources at the temple to boost your reputation points. At level 5, 10000 of each resources will yield you +1 reputation point.

You can also build rare buildings. Some of those will give you a reputation boost as well.

Is reputation important? Maybe yes, maybe no. If you are already in an order, and are maxed out in getting vassals (or if you don't want any vassals), then reputation does not matter at all. That's just my two bits.

There are several things that you can do that will hinder your reputation points: (-50 for declaring war, -10 for breaking an alliance, some negative points for leaving your orders, -20 to build a mark tower (but you get it back once you do something with that mark tower)). If you are in the negative, you get 1 point back per day until you reach zero reputation points.

If you have more than zero reputation points, there are no benefits whatsoever other than bragging rights. It doesn't help you or hurt you in any other way whether you have 0 points or 10000 reputation points.