I'm just going to assume the Middle East means the Levant, Mesopotamia, and the Arabian peninsula. All that came with the Ottoman conquest of the Mamluks of Cairo and fighting the Safavids of Persia.
The Mamluks were conquered in 1517, with the modern Ottoman army equipped firearms defeated the Mamluk knights. This gave them the Levant/Syria, Egypt, and the Arabian peninsula.
Then the Ottomans fought the Safavid Persians and took Baghdad and Basra later on later on. Like the Mamluks, the Ottomans had the technological advantage and rolled over the Persians fairly easily.
Of course, this kind of leaves central Arabia out, which has never really been part of the Ottoman Empire in full, because it was a ridiculously difficult region to conquer and occupy, but we're counting it here, because this is pre-oil and it's just not that important at this moment.
As to why the Ottomans took over the Middle East, there's a lot of reasons.
They were on an expansionist trend at the moment. It was a growing empire and the region was immensely rich in trade and culture.
Conquering the Mamluks and the Arabian peninsula as a consequence gives them Mecca and Medina, so the Ottoman Sultans could definitively say that they were the protectors of Islam, which was a useful thing in the process of consolidating their power.
Related to number 1 and 2, conquest of Baghdad and Basra meant a lot of Sunni Muslims were freed from the rule of the Shia Safavids, which let them gain a loyal enough populace in another wealthy region in both agriculture (because cradle of civilization) and trade.