Statutory refers to something that is related to a formal law or a statute, and non-statutory is essentially another term for common law. If something is statutory, it is based on laws or statutes. If something is non-statutory, it is based on customs, precedents or previous court decisions.
One of the most commonly used instances of the word statutory is in the phrase statutory rape. This phrase refers to a consensual sexual act between an adult and a minor. The inclusion of the word statutory in this phrase refers to the fact that the encounter is considered rape under the law. However, it is not necessarily rape in the sense of being forced to perform sexual acts against one's will.
Another case in which the words statutory and non-statutory are used is in the discussion of stocks. If someone purchases a stock through an employee stock program or an incentive stock option (ISO), he is buying a statutory stock. If he purchases stocks through another entity or program, he is buying non-statutory stocks. Both statutory and non-statutory stocks are taxed as capital gains, but the way the IRS values these stocks is different.
Although the word statutory is still used regularly, the word non-statutory is not used as often, as most people simply use the phrase common law.