To add to Rupert's answer, 4G is a very different technology as compared to 3G and was made possible practically only because of the advancements in the technology in the last 10 years. In most laymen terms, the technology is compared in terms of speeds. To show a difference of speeds, lets look at this picture below:

The standard body that has made 3G and 4G possible, is known as 3GPP. They do updates in terms of releases that can last anywhere from 2 years to 1 year. 3G was defined in Release 99 (Rel-99). The data rates with pure 3G were in real terms a bit of shambles. They quickly realised and fixed them in Release-5 (Rel-5). The data rates became a theoretical maximum downlink (DL) of 14Mbps and uplink (UL) was still the same, 384kbps. In Rel-6 this UL rate was improved to 5.76Mbps theoretical max. The DL data rates increase feature was known as High Speed Downlink Packet Access (HSDPA) and the uplink one was correspondingly HSUPA. Together they were referred to as HSPA.

At this point you may be thinking, how did 3GPP jump from Rel-99 to Rel-5? Well the intention was Rel-99 for 1999 and Rel-00 for year 2000, etc. but they soon realised that it will take much longer than just 1 year so they abandoned this in favour of Rel-4, Rel-5, Rel-6, etc. Rel-00 was the Rel-4.

Coming back to the original data rates discussion, by Rel-8, the data rates for HSPA were improved to 42Mbps DL and 11.52 Mbps UL. LTE, that is known as 4G was standardised for the first time in Rel-8. Its theoretical maximum speeds were 300Mbps for DL and 75Mbps UL.

Now, even though the LTE was part of Rel-8, its just started being deployed. The HSPA camp were not sitting idle so they have improved some of the things in the HSPA technology to improve their data rates. So if we do a comparison of LTE Rel-8 and HSPA Rel-11 we see the following:

People are ready to point out that with HSPA now we can achieve data rates as much as 672Mbps DL and 70Mbps UL. This is not very different from LTE. True, as long as we say that LTE will stay on Rel-8.

New technologies are being introduced in LTE as well so if we do a true like for like with HSPA and LTE both Rel-11, we see this final chart

As you will notice that LTE DL (3Gbps) and UL (1.5Gbps) beats HSPA DL (672Mbps) and UL (70Mbps) in terms of data rates any time.

It should be noted that as I have been saying, these are all theoretical rates per cell. The real data rates that a user will receive will be far less. There are also finer technical details that I wont go here which means that the practical rates can be quite limited.

I hope you get an idea about the rates though.