Can someone explain what are the difference between these processors?

Intel Core 2 Duo
Intel Pentium Dual-Core
Intel Celeron
Intel ATOM

Celerons are the single core equivalent of the pentium single core with the onboard cache stripped. The new Pentiums have less cache than the Core 2 Duo and generally lower performance. Having only 512kb per core is tiny and will seriously affect multitasking. If you work with video in particular, I would suggest keeping to the proven Core 2 Duo line. Testing I've seen suggests that with multimedia and 3D gaming, the Pentiums are appreciably slower thanks to the smaller cache. The Intel Atom is significantly smaller the its core 2 duo counterpart and requires significantly less power to operate. It also sacrifices performance for power consumption.

Sneakycyber explained the differences well but here is some added information. The Core 2's are newer and come in dual and quad core varieties. These are being replaced by the i7 and the soon-to-be-released i5 CPU's. Most users wanting performance will go for newer CPU's, such as the Core 2's, i7's, and AMD's CPU, the Phenom II's. The Pentium's are the lower end cousins and are typically avoided by gamers. The Celeron's are designed for notebook or low-cost PC's. Atom CPU's are meant for netbooks or discount PC's where the amount of power needed to run the CPU is a major factor. Intel's rival AMD produces chips similar to theirs at a lower cost, but they are often not quite as advanced. Gamers or people building sub $1000 or $1500 generally choose the AMD CPU's. Currently AMD's Phenom II X4 line of CPUs is aimed at Intel's Core 2 CPU's.