H stands for HSPA or "High Speed Packet Access". As NazNomad correctly stated, it is in essence 3.5G or rather 3G+
Because you have upgraded, the phone you now have is capable of utilising newer technologies to achieve better upload and download rates of data. In terms of UK phones, the technology to access mobile data has evolved as follows:
WAP > GPRS > EDGE > 3G > HSPA (3G+)
The connection your phone uses will also depend on your signal strength and cell access. If your signal strength drops, you might find you phone reverts to 3G, Edge or GPRS. Also, having a HSPA signal doesn't guarantee fast data rates, particularly if the cell your phone is trying to access is working at or near capacity.