The belief that once a person is saved there is nothing that can be done to cause them to lose their salvation. As a point of Calvinism, this is known as perseverance of the saints.
While this is a Calvinistic belief, there are many who are not Calvinists who hold to the belief. There are numerous approaches taken in defense of this belief.
1. You are sealed with the Holy Spirit upon salvation and absolutely nothing can be done to break that seal. Therefore you cannot lose your salvation.
2. As a Christian God will supernaturally give you the ability to maintain your salvation. Passages speaking of those who overcome are in reference to all believers because God will allow them to persevere. This is sometimes also called the preservation of the saints.
3. Because God elected the believer, He would not elect someone who would later lose their salvation. While loss of salvation is theoretically possible, God would not elect those who would later lose their salvation.
The alternative is that man can indeed lose his salvation and he must be faithful until the end. This is known as conditional perseverance.
Also known as: perseverance of the saints, preservation of the saints, once saved always saved, OSAS
For more information, see the article Eternal Security.