Why were the Arabs able to conquer territory quickly.

Their imperiors were the succeeders

They weren't so successful at conquering Europe or China. Of course, one can blame the long supply lines, but in these cases their adversaries were also determined to repulse them.

In contrast, Byzantium and Persia were exhausted from mutual warfare. Tribes related by kinship to Muslim Arabs had served as mercenaries during this period, so there was a lot of tactical knowledge available.

The Byzantines retreated to the highlands of Anatolia upon losing their lower-lying provinces to the Muslims. I am not sure if they launched a determined counter-attack. The Persians did, but they could not fight coherently.