Integrity is the property of an asset that states that it remains intact. In other words, it requires that only authorized parties are able to modify the data. It is one of the three elements in the classic CIA triad of security properties, alongside confidentiality and availability.
Typical measures to enforce integrity include physical protection (e.g. keeping papers in a locked safe, or writing to read-only media). Cryptography can help maintain integrity; in particular, to verify the integrity of some data, it is enough to compare its hash against a known value (the hash must still be obtained reliably).