Core i3 Series
Intel's Core i3 processor line has always been a budget option. These processors remain dual-core, unlike the rest of the Core line, which is made up of quad core processors. Intel's Core i3 processors also have many features restricted.
The main feature that is kept from the Core i3 processors is Turbo Boost, the dynamic overclocking available on most Intel processors. This, alongside with the dual-core design, accounts for most of the performance difference between Core i3 processors and the i5 and i7 options.
Core i3 processors also lack Intel's vPro technology virtualizaton and AES encryption acceleration technology. These are features unlikely to appeal to your average user anyway, and are instead targeted towards enterprise users. Still, the lack of these features should be kept in mind.
One feature that Core i3 has - and i5 doesn't - is hyper-threading. This is Intel's logic-core duplication technology which allows each physical core to be used as two logic cores. The result of this is that Windows will display a dual-core Core i3 processor as if it were a quad-core.
Finally, Core i3 processors have their integrated graphics processor restricted to a maximum clock speed of 1100 MHz, and all Core i3 processors have the 2000 series IGP, which is restricted to 6 execution cores. This will result in slightly lower IGP performance overall, but the difference is frankly inconsequential in many situations.