Like so much else in Judaism, that’s going to vary from person to person, and among individual observances for one person.
Some people observe some mitzvot (basically, rules) because that’s just how they’re used to doing things. They don’t eat cheeseburgers because they never ate them before and don’t find them terribly appealing, just like my parents don’t find sushi appealing or most Americans wouldn’t eat bugs given the opportunity. They go to a Passover seder because they remember going to them when they were younger and would feel they had missed out on something if they didn’t (like how some ex-Christians do with observances associated with Christmas this time of year). They wear yarmulkes to synagogue because they’d feel incompletely dressed if they didn’t.
Some people do observe some mitzvot because of family or social pressure. Some people start observing some mitzvot they didn’t observe previously when they become parents, as a way of setting a good example for the kids. This kind of thing is hardly unique to Jews. There will probably be a fair number of people going to Christmas services tomorrow night for the exact same reason.
Some people observe some mitzvot because they like to. Frankly, I like having an excuse to not do errands, chores, or work brought home from the office on Saturday. Things like lighting Hanukkah candles are fun.
Some people believe that God will punish them, either before (sort of like karma) or after they die, if they don’t observe certain mitzvot. There’s no official Jewish dogma or universal belief on this kind of thing. But it’s human enough to think you might be punished for breaking the rules.
Some people believe that observing the mitzvot makes the world a better place, and makes the world more like God wants it to be.
People being the complex beings we are, the same person might have different motives for observing two different mitzvot. Or someone might have more than one motivation for observing one mitzvah.
In Judaism, it doesn’t matter why you observe a mitzvah, just that you do. If you rest on Shabbat because you’re lazy, that’s just as good as resting on Shabbat to make the world more like God wants it to be. The doing is the important thing, not the reason why you’re doing it.
If you sin in a way that harms another person, you are supposed to apologize to that person and try to make restitution. For sins that don’t harm another person (things like not keeping kosher), fasting and praying on Yom Kippur atones for them. It doesn’t atone for sins that harm others, unless you’ve tried to make things right with the other person before. Of course, you’re also supposed to try not to commit the same sin again. We’re not expected to confess our sins to anyone else, and we don’t have anything like the Catholic distinction between mortal and venial sins, though most Jews would probably agree that some sins are worse than others.