These are commonly known as "The Doctrines of Grace" or "The Five Points of Calvinism." They are a summary of what the Bible teaches regarding sin and salvation, and were John Calvin's rebuttal to the heretical doctrines of Jacobus Arminius (in the 1500's).
Total Depravity refers to the condition of all of us by nature ever since the Fall of Adam (Rom 5:12)---we're spiritually dead (Eph 2:1-5), and in bondage to sin to the point that there is nothing good in us (Jer 17:9; Rom 3:9-20, 7:18), and we couldn't change it even if we wanted to (Jer 13:23; Rom 8:7).
Unconditional Election refers to God's choosing and predestinating a particular people to save before he even made the world, and not based on anything in or about them, but by his free grace. (Eph 1:4-6, 11-12; Rom 8:29-30, 9:11)
Limited Atonement refers to the purpose of God in sending his own Son to die for a particular people, those whom he chose and predestinated unto salvation. (John 10:11,15, 17:9; Eph 1:3-7)
Irresistible Grace refers to the almighty, irresistible power of God the Holy Spirit in drawing sinners to God, by changing their wills so that they will receive Christ by faith. (Psa 110:3; John 6:37,44; 10:16)
Perseverance (or Preservation) of the Saints refers to the preserving power of God which ensures that those who are redeemed by Christ, and called by Christ, will persevere in the faith. (John 10:27-29; Rom 8:29-30, 34; Heb 7:25)
Also, just a general question: Do you believe the Bible is open to interpretation?
No, the Bible is a definite declaration of divinely inspired and authoritative truth. And even the most obscure passages are made clear when you consider that it all has to do with Christ and the cross.
Also,
How do you know without doubt that you are one of the select few?
The short answer is this: The Bible plainly declares that those who trust in Christ for all their salvation, apart from their works, are just in God's sight, and are the children of God.
"But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:
Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God." - John 1:12-13