The D3100 and D3200 are Nikon's "entry level" DSLRs. Despite the "entry level" name, one could use either one of these cameras for professional work, no doubt--just as long as you have vision. The D3200, which came out this year, is Nikon's replacement for the D3100, which was released in 2010.
The cameras are very similar on the outside, but internally they are much different. The D3100 has an APS-C sized sensor with 14 megapixels and uses Expeed 2 image processor. The D3200 has an APS-C sized sensor with 24 megapixels and uses Expeed 3 image processor. DxOMark, which scientifically tests digital cameras, ranks the D3100 52nd best and ranks the D3200 11th best (right up there with cameras that cost several thousand dollars!). As you can see, the D3200 scores much, much higher than the D3100! Internally, the D3200 is definitely superior.
So why would anyone buy the D3100? Because it's still a perfectly fine and capable DSLR and it costs less than the D3200. The D3100 with a kit lens has an MSRP of $650, but if you shop around and exercise some patience, you can find it for as little as $500. You should have absolutely no problem finding it for $550. The D3200 has an MSRP of $700 and, because it's new and popular, you won't likely find it discounted.
If your budget is strictly tight, the D3100 might fit that budget while the D3200 won't. However, if your budget allows an extra $150 or $200, the D3200 is the camera to get.