Apologetics in general is a reasoned defense of beliefs. Presuppositional apologetics is a reasoned defense of Christian beliefs based on initially recognizing what one's presuppositions are and reasoning from those starting points . For instance, my presuppositions are that God exists and He has given us His Word in the Bible which is absolute truth. So I use the Bible as the basis for how I think, interpret evidence, explain the world around me, and how I read the Bible.
An atheist’s presuppositions are that there is no God and that truth is relative to the individual. The atheist believes that man ultimately decides what the truth is. His presuppositions predetermine how he thinks, interprets the evidence he encounters, views the world in which he lives and how he views the existence of God and the Bible. When challenged by atheists on their beliefs about the faith, Christians too often believe they must first prove the Bible and the existence of God. This defensive posture shows that they don't understand the approach known as presuppositional apologetics.
Presuppositions are beliefs everyone has. They affect how we think, view the world around us, interpret evidences and our understanding of God and the Bible. A presuppositionalist believes the Bible is the Word of God that defines reality. This is his starting point for evaluating everything. In theology this is known as an axiom. It is defined as a statement or proposition which is regarded as being established, accepted, or self-evidently true. An axiom is often used in logic. It is a proposition that is not susceptible to proof or disproof; its truth is assumed. The Bible takes this stance, assuming God’s existence to be true and not something that needs to be proven .
Presuppositionalists believe the battle one encounters in defending the faith is not over evidence. It is over philosophical starting points: presuppositions. Everyone has presuppositions. Knowing this can be an asset when it comes to defending the faith. Christians who abandon the Bible for the sake of defending their faith in a supposedly "neutral" discussion are making a mistake. There is no neutrality in these discussions. The prophets and the apostles never tried to prove God’s existence. They started by assuming God’s existence, and they always reasoned from Scripture. Knowing everyone has presuppositions is used as a tool in the defense strategy of the presuppositionalist. They can point out to the atheist that their discussion are not neutral and show how their arguments begin with their own presuppositions - not evidences. From there the Christian can take the offensive and show how their reasoning is flawed because their presuppositions are flawed.