Many reasons explain why the Islamic military expansion was made in a fast and extended way across different continents.
The first and major key point was the constant wars between two great empires of the era (the byzantine and persian) that led to their mutual debilitation, this allowed Islam to start with an important advantage.
Besides this, the Koran teachings (where the expansion of the ¨word of God¨ across the known world was practically asked) and Islamic people will (very religious and highly motivated to conquer due to this).
The effects of the expansion were notable, giving a lot of power to the Islamic empire for a considerable amount of time against important enemies, like the European catholic kingdoms).