Out of all the ways you can play Path of Exile, the race league seems to be the most intriguing due to how it stands out in the action role-playing game genre, or at least when it first came about. It seems to make sense that you can turn speed leveling into a focal part of gameplay, but it was Grinding Gear Games that took it as far as they did. With that in mind, novice players may want to get into it, and there's even an official guide on racing in the Path of Exile forums right now.
However, maybe even that's a bit too long and complicated for some. There's a lot of details to go through with racing in Path of Exile, especially with how it is now. For those who are in need of a guide for racing that's easier to understand for the less experienced so that they can be brought up to speed, then here's an abridged version.
There may be a whole lot of race leagues in the game, each with its own set of rules and concepts, but the most basic thing about racing is it's basically speed leveling—getting as high of a level as you can or reach a certain achievement as quickly and efficiently as possible. Racing is all about efficiency, and game knowledge is what lets a player do just that. When you're an expert racer in Path of Exile, you already know exactly what you need to do in each step of your race and have no need to stop and smell the roses to explore and look for what's next.
Learning about the game, planning your approach, determining the character build and Path of Exile items of choice, and being able to play smoothly all go into racing. Once you have all that down, which should take you a few tries, you then get more into the distinctions between all the different race leagues. Each has a different goal in mind, which you should then plan and play for accordingly. Reaching for that goal is pretty much what makes racing fun in Path of Exile.
These leagues do have their own challenges, as well as their overarching conditions. For instance, boss kill races are pretty much what it says in the name—you must kill the indicated boss as quickly as possible. That means you have to level up, gear up, and kill the boss all in one run.
There's also the cutthroat league, which is basically a race league with PvP of sorts. You may enter another player's instance by Ctrl-clicking a waypoint or doorway and try to kill whoever is in it. Those who are able to do so stand to gain experience and the slain character's non-gem PoE items.
There are a lot more like those, with each race season bringing in more unique experiences for players to try out. What makes racing interesting in Path of Exile is how diverse and original each race league can be.