You can implement any gate from NAND or NOR gate but you can't do so with AND or OR gate .In addition the NAND and NOR implementation(in popular logic families) is more simple than AND or OR gate .
In addition,a NAND gate has the smallest propagation time delay among other gates (except for the inverter). Thus, it's the basic building block of all logic circuits.
NAND and NOR gate more popular because of all other gates can realized by using NOR gate only or NAND gate only. So they are called universal gate. This is possible by solving Boolean equation of gates using Demoragan’s law. Even NAND gate is realized by NOR gate and vice versa.
NOT, NAND and NOR are the base of modern digital design.
The reasons are:
1. NAND and NOR have smaller area than AND and OR
2. NAND and NOR are faster working
3. All of more dificult devices are built from theese elements. Look for any trigger.
for two reasons :
1)NAND gates use fewer transistors than AND gates and circuit implementation using NAND gates will result in a smaller area in the IC.