An electron is a fundamental particle, it cannot be broken into other smaller ones.
The family of fundamental particles is called the standard model
http://en.wikipedia.org/wiki/Image:Particle_ch art.jpg
Why the different particles have the particular properties that they do, charge, mass, etc. is still unknown.
We may though be close to finding out why it has the mass that it does.
There is a theoretical particle called the Higgs particle, not yet proven to exist but this particle would "give" mass to all the others.
Right now there is an experiment at Cern nearing completion that might just be able to find it if it exists.
I know this sounds hard to get to grips with - other people think so too - that's why in 1993 there was a competition for people to explain on 1 side of A4 "What is the Higgs boson and why do we want to find it?"
You can see the winners here:
http://public.web.cern.ch/Public/Content/Chapt ers/AboutCERN/CERNFuture/WhatLHC/WhatLHC-en.ht ml