It differs per MMO, I can tell you that. But in the case of GW2, you are free to do whatever you want.
You can choose to ignore the events or to help completing them. You can even help partially and run out halfway, just to see a "Event failed/succeeded" and a badge popping up.
Completing events often award you some money, some experience and some karma. It is true that by completing events, you usually level up the fastest and gain karma the fastest way. There are some areas you'll have to walk through for 10 minutes and you won't see an event popping up, so it's kind of balanced out with other ways to gain experience and karma.
Going back to which you should choose, I'll tell you again: you are free to do whatever you want. Decide for yourself what you'd like to complete. Do you wanna progress the story? Progress the story then. Would you like to achieve the Daily achievement and you need to do a few Shiverpeak events? Go complete some Shiverpeak events! Are you up for exploring some maps? Try to score some Vista's and Skillpoint's then!
There are a lot of personal goals to be completed in this game. For example, I'd like to complete all of the exploring, jumping puzzles and dungeons. After this, I'd like to save up for my legendary weapon. Some goals should be completed within a month from now (have been playing for a while), while others will probably take a few months, if not years, to complete. That's the point of a MMORPG, or at least this one: you'll probably never fully complete the game. Especially not with the new content popping every month or two.
As for the display on your map. The green star indicates which way to go for your Personal Story. Next to this, you'll have orange text and yellow text events.
Orange text indicates a dynamic event. Dynamic events are cyclical in nature and the events are generally chained together. Events do not necessarily follow a fixed schedule, and may only trigger if certain conditions are met - for example, if a snow storm strikes an area, or if night falls on a graveyard. Once an event has triggered, it will continue to progress whether or not players participate in that event. Although the cyclical nature of the system means that consequences are ultimately temporary, event results can persist for days, weeks, or even months until a player comes along and does something to progress the chain of events. Each event has an NPC associated with it with whom the player can talk to learn more about the story and lore behind the event.
In addition to single events, several common types of event chains can be observed: Chains of events which progress linearly as the players participate in them, and repeat after short while; Branching events which may end up one way or another; Conquest-like battles, often part of meta events, in which players side with allied faction to fight enemies and attempt to capture multiple locations or take down several enemy forces, while the opposing force seeks to do the same.
The icons of these dynamic events differ. You can find out what they mean on this Guild Wars 2 Wiki page.
Like said before, the yellow text are meta events. A meta event is a series of dynamic events that tells the story of an explorable zone. A meta event might tell the story of a norn area in danger of being corrupted by the Sons of Svanir, or a human region constantly threatened by centaur armies. Meta events are meant to provide immersion, as well as orientation about the state of an area.
There are generally two or more meta events in each zone. These meta events are usually made up of 5 to 20 events chaining and branching in various directions.
Meta events are displayed in the event assistant, framing the actual dynamic event that marks the state of the meta event. They stand out because they are displayed even if no events are currently running. However, unlike dynamic events, meta events are neither completed nor do they provide experience points or rewards of their own. However, if players succeed at certain meta events, hidden areas of the world may become accessible for a period of time.
TLDR: There is no 'better' event to choose from. Pick the one which you'd like to help out with, or don't help at all. You are free to do what you want in GW2, and none of the choices you make is the bad one. Everything has effect in the game. If you gather a resource, you gain xp, if you revive someone, you gain xp, if you complete (or fail) an event, you get xp as well. Just enjoy the game and find out the beauties the game has 'hidden' all over.