Discuss and learn French: French vocabulary, French grammar, French culture etc.
OK, there are kind of two levels of answer you can give here. The simple, pragmatic answer is just to say that there re a few French verbs that are 'reflexive' "just because they are". If you take se to basically mean "oneself" (or "one another"), then there's no terribly logical reason to expect rire to mean "to laugh", but se rire (de) to mean "to make fun of". Similarly, you could tie yourself in knots trying to work out why the verb meaning "to cry out" is s'écrier and not simply écrier etc etc.
Now, taking a historical perspective, it is possible to offer a slightly more satisfactory explanation. The thing is that the restriction on se meaning "oneself" or "one another" (or being used to form a kind of 'ergative' or "semi-passive" verb, as in cela ne se fait pas, la salle s'est remplie de spectateurs etc) applies to modern French. But historically, this "reflexive" construction took on a slightly wider set of uses, as indeed it still does in modern Spanish.
So, once upon a time in French it was more common to say e.g. soi aller, soi partir etc (cf modern Spanish irse, partirse, bajarse...), as a way of lending some kind of emphasis-- perhaps to simultaneously indicate a notion of movement and also the result of that movement. Whatever the exact distinction that Old French speakers perceived between e.g. soi partir vs partir, it's essentially been lost today.
However, we're left with a few relics of this "emphatic" construction, including s'(en) aller (once upon a time, the en would have had more of its literal meaning of "from this/that place"; nowadays, it's pretty much fused with aller, and you'll hear people say e.g. "Il s'est en allé" rather than "Il s'en est allé"; cf en mener > emmener, which has already gone through this process).
You'll find a few other examples in modern French where you can just about see se as meaning "emphasising the deliberate/prolonged action of the subject" or something like that. Compare, for example:
Il s'est approché de moi.
vs Ça approche, ton anniversaire.
Il a décidé de le faire. = "He decided (in a matter of fact way) to do it"
vs Il s'est décidé à le faire. = "He decided (in a determined manner after due consideration) to do it"
Le roit meurt. = "The king died" (using a historic present)
vs Le roit se meurt. = "The king is/was dying, the king is/was in the throes of death"
Ah, Neil's reply is much nicer than mine :) My answer comes from what I've learned in my studies. It is rather simplistic, though.
Thanks Neil that's a great explanation. Interestingly the discussion started when my friend who is learning Spanish asked why one says: me voy. I tried to use my French knowledge to explain but was a bit stuck. I'll send him your explanation which also explains the Spanish! Merci and gracias
I believe that when you use aller with a reflexive, it means "to go away" rather than just "to go". So, in a way, it means almost the opposite, because it means to leave a place, rather than go to a place when you have the reflexive pronoun.