Simply...
Israel pioneered an application of drones, when most other countries considered the drones as "toys"
The major background of active UAV development and deployment was the Yom Kippur War in 1973 when IAF suffered big losses to SAM and failed to destroy them mostly due to lack of up-to-date real time intelligence. Israeli developments in the UAV area had finally played huge role in the Operation Mole Cricket 19 in 1982. UAV were playing both as decoys and what is probably more important gathered an up-to-date intelligence information on SAM sites.
I suggest you to start from Wikipedia - and follow the references.
Israel is the most innovative in UAV are because:
- It needs up-to-date intelligence probably more than any other country (i.e. bad neighbor, take a look on major wars, not including smaller operations: 1956, 1967-1970, 1973, 1982, 2006)
- It can't afford human casualties, unlike its neighbors
So it is natural that Israel is major leader in this area