A single nucleotide polymorphism is single because it is one out of millions or billions, is nucleotide because it consists of three things (a nucleobase, a phosphate group and a sugar), and is a polymorphism because it is different from what is expected in the genome. In other words, single nucleotide polymorphism (SNP) means one single change in the genome. For reference, the human genome is about three billion nucleotides long.
Sometimes one single mutation/SNP in the genome can have a life altering effect. Other times, entire ranges of thousands of nucleotides can be removed from a genome without any obvious impact. In other words, some SNPs are more important than others.
In science, important SNPs can serve as markers/tags for disease or even positive characteristics. Scientists are in search of important SNPs because these SNPs have commercial and medicinal value and are useful in observational science too (the type of science that focuses on describing things and leaving it at that).
In diagnostics, SNPs are useful because if an organism (or a person) has a certain SNP you can say for sure that person also has some characteristic. These characteristics (also called phenotypes) are usually a disease because a lot of funding in science is granted for the study of diseases. Marker assisted selection (MAS) is also a popular application. An example of MAS is where someone snips off a part of a sapling and looks for a SNP that is associated with high yield. In this way the person doesn't have to wait for the plant to mature before knowing whether it would be a high yielding specimen (e.g. have many grapes).
It is important to note that groups of SNPs can contribute to a characteristic in an organism -- characteristics that would otherwise not be present if any single SNP or some of the SNPs in the group were not present.
Single-nucleotide polymorphisms (SNPs) constitute one of the well-known units of genetic variation, and they provide powerful tools for a variety of medical genetic studies. SNPs may be located in the coding sequence of genes and in the regions between genes; thus, the functional consequences of SNPs may involve changes in amino acids, mRNA transcript stability, and transcription factor binding affinity. This genetic diversity is of interest because it explains the basis of heritable variation in disease susceptibility, as well as harbors a record of human migrations. SNPs can serve as genetic markers for identifying disease genes by linkage studies in families, linkage disequilibrium in isolated populations, association analysis of patients and controls, and loss of heterozygosity studies in tumors. Most disease studies have reported disease-associated SNPs but have usually underestimated the influence of individually nonsignificant SNPs. Therefore, a SNP–SNP interaction is a genetic association that can be used to determine the effect of a single genetic variation associated with other genetic variations. The investigation of SNPs associated with a disease trait, disease-relevant genes can be identified to provide insight into genetic associations and epistasis.