The reasons differ depending on who you talk to...

1) Homeric glory, he was trying to immortalize himself through deeds, hence the great risks he took

2) Religious crusade, in retaliation for the desecration of Greek holy places during the Persian wars

3) Desire to see the eastern world, driven by cursiosity instilled in him by his time with Aristotle

4) He was incredibly in debt and needed to money, war equals money, especially the thousands of talents of gold in the Persian coffers

5) He truly believed he was devine, and repeatedly strived to establish himself as a god. Only by conquering the Persians could he accomplish a deed worthy of divinity

Some historians believe that as he was more and more successful, his motives changed as well. Tons of great readings out there with all kinds of different opinions.