BLAST finds region of similarity between biological sequences. The program compares nucleotide or protein sequences to sequence databases and calculates the statistical significance. It can be run on the web or as a standalone desktop application. There are specialized BLAST searches for query comparisons such as GEO to look for matches to gene expression profiles OR CD-search to find conserved domains in your sequence. BLAST is a software, not a database in the traditional sense, but it does perform sophisticated searches like you do in other databases.
BLAST is a registered trademark of NCBI and you must cite it if used in publication
Altschul SF, Gish W, Miller W, Myers EW, Lipman DJ., "Basic local alignment search tool". Journal of Molecular Biology. 215(3): 403-410 (1990).
Finding a statistically significant match based on sequence similarity allows for researchers to:
(From Lecture Notes, Librarians Guide to NCBI, Librarians guide to BLAST)
Query: unknown sequence
Subject: known sequence from database
Identity: the degree to which sequences are exactly the same
Similarity: the degree to which two or more sequences resemble each other; can imply similar functions with caveats
Homology: sequence similarity from a common ancestor