In simplest terms, as used in the Bible, the elect are those selected or chosen by God and/or Jesus--followers of Christ.
Used in multiple verses, the term also signifies those (Christians) who will be raptured to heaven during the end times;
And he shall send his angels with a great sound of a trumpet, and they shall gather together his elect from the four winds, from one end of heaven to the other. (Matthew 24:31)
Being one of the elect doesn't just mean you believe, but that you are wise for doing so, as implied by Jesus in Matthew 24:24:
For there shall arise false Christs, and false prophets, and shall shew great signs and wonders; insomuch that, if it were possible, they shall deceive the very elect.
The elect also don't just have salvation and a future with God and Christ to look forward to. After Christ's Second Coming, the elect will serve in his earthly kingdom:
Blessed and holy is he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God and of Christ, and shall reign with him a thousand years. (Revelation 20:6)