God's elect are those who are predestined to salvation [determined beforehand]. God chooses those who will be saved. They are the elect of God.
Some believe this means that God, through His omniscience, knows those who will in the course of time choose of their own free will to place their faith and trust in Jesus Christ for their salvation.

Others believe that God not only elects His people, but also grants to these the faith to believe. In other words, salvation is based on grace alone.
Who then, makes the ultimate choice in salvation – God or man?
The answer is:
God is in control. He freely chooses those whom He will save. He not only elects those whom He will save, but He actually accomplishes their salvation. Rather than simply making salvation possible, God chooses those whom He will save and then saves them. This view puts God in His proper place as Creator and Sovereign.
There are certainly many who view this as unfair, but God word tells us in Rom 9:14-18 that He is in control of His entire creation, including man! And, the fact that He is in control flows from Rom 8:33-35 – where He tells us that we are secure in Christ.
Psalm 118:1