It is simply the name that Intel has given to the CPU architecture (design).
Lynnfield/Bloomfield were the 1st generation Core i3/i5/i7 CPUs. Sandy Bridge (SB) is the 2nd generation, while Ivy Bridge (IB) represents the 3rd generation Core i3/i5/i7 CPUs.
The difference between IB and SB are mostly minor. The main difference is the improved integrated graphic cores; Intel HD 2500, and HD 4000 depending on which model you buy. The Intel HD 4000 (IB) is about 35% more powerful than the Intel HD 3000 (SB). Sounds impressive, but the is simply going from the performance of the desktop Radeon HD 5450 to the Radeon HD 5550. This is the most dramatic change and likely meaningless to most gamers since they plan on installing a graphics card anyway which deactivates the Intel HD 4000.
On average there is a 6% performance improvement from SB to IB; assuming the same clockspeed. In CPU intensive programs like video encoding you would be able to see that small improvement especially if you are encoding a long movie. But in games, you will not notice any difference.
Power consumption has been reduced. Not a big deal for desktop CPus, but it will improve battery life for laptops.
There are other difference, but basically are meaningless to the average user / gamer.