The Ottoman Empire had both specific and general military objectives. As with all empires, the Ottomans looked to end threats to their holdings, to take colonies or subject rival countries and nations and to secure wealth and resources for the homeland. This is the nature of all empires and the Ottomans were no different.
Specifically, they primarily wanted to conquer the neighboring Byzantine Empire (which they eventually did), secure the city of Constantinople permanently against crusaders (renamed Istanbul), eliminate through genocide Armenian Christians within the empire's borders, and establish a hub of coastal control along the Mediterranean Sea. This would give them security within their borders, and access to trade and resources.