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SHA-1 (Secure Hash Algorithm, 1st version) is an algorithm which converts a given sequence of characters into another unique sequence of characters, with a fixed length, called "hash". For instance, the SHA-1 hash of the word password is 5baa61e4c9b93f3f0682250b6cf8331b7ee68fd8.
These hashes are mostly used to validate file integrity, to encrypt sensitive data (like passwords), and to generate unique identifiers.
SHA-1 hashes are theoretically impossible to reverse directly, ie, it is not possible to retrieve the original string from a given hash using only mathematical operations.
Most web sites and applications store their user passwords into databases with SHA-1 encryption. This method appears to be safe as it seems impossible to retrieve original user passwords if, say, a hacker manages to have a look at the database content.
Unfortunately, there is a way to decrypt a SHA-1 hash, using a dictionary populated with strings and their SHA-1 counterpart. As most users use very simple passwords (like "123456", "password", "abc123", etc), SHA-1 dictionaries make them very easy to retrieve.
This website uses a SHA-1 reverse dictionary containing several millions of entries, which you can use with SHA-1 hashes from your application.