H1, H2 and H3 system replaced the past AO, A and S standards.
H2 is the 'normal' A level standard subject.
H1 has half the breadth but same depth as a H2 subject (i.e. you learn half the things but they still test them at the same difficulty anyway)
H3 is like your S paper except that some say it is more difficult than the S paper standard. Think of it as additional cirriculum in addition to your H2 subject. It requires you to have passion and motivation to complete that H3 module (I can personally vouch for it). You will need to offer a subject at H2 level before being able to take it at H3 level. For example, you can't offer H3 Chemistry when you offer H1 Chemistry. To take H3 Chemistry you need to offer H2 Chemistry.
Of course, most people take only 1 H3 subject but I have quite some friends who take 2. There are external H3 modules which can be used to replace your MOE H3 modules but these details will be made known to you in JC.
Any doubts, check
http://www.seab.gov.sg