The translation of the word minyan is "count." Jewish law states that a minimum of 10 men over the age of 13 are required for what is called a davar shebekedusha—a holy matter, such as certain parts of prayer or the liturgy of a wedding.
While the number ten is common in various contexts (10 commandments, 10 fingers on the hand, 10 toes), the Torah teaches that at least 10 men are needed to form a congregation, as described in the story of the spies Moses sent to the Land of Israel. Of the twelve men who went, two returned with a positive account and ten with a negative one.
The verse says that God exclaimed, "How long will this wicked congregation continue?" referring to the ten men who had spoken evil. From this, it is understood that a congregation consists of at least ten men.