There are three major types of survival analysis techniques, differing in the assumptions that need to be made. As a metaphor, a pair of trousers is a parametric model. More exactly it is a 2-parameter model, one on waist circumference and one on leg length. In contrast, a skirt with an elastic waist is a non-parametric model. This is unlikely to fit well but it never fails badly. If you don't know or if you are unwilling to guess the body size (the data), you can buy a skirt with an elastic waist (a non-parametric model). If you are confident that you know the body size quite well, you can buy a pair of trousers (a parametric model) and get a better fit. A semi-parametric model is a trade-off between the two extremes.

An introductory text covering all three types of techniques plus a medical focus is:

Collett D. Modelling Survival Data in Medical Research. London: Chapman & Hall, 1994.