Security refers to ways of protecting sensitive resources from unauthorized access. This is usually done with a combination of authentication - to prove an individual's identity -, and authorization - to grant or deny an operation on a resource. Most security measures also involves some form of cryptography: secure digests to preserve data integrity, data encryption mechanisms to protect data access from individuals without proper authorization and digital signatures to prove authenticity of some sort.
Authentication is the process of validating an individual's identity. It's about finding out if an individual is who he/she claims to be. This is done by presenting some proof of identity, which usually can take the form of username/password, digital signature, etc. The idea is that each individual can be recognized by unique information that differentiates him or her from other individuals.
Authorization is about, once a user has been authenticated, determining if hs/she is authorized to do something. A successful authorization results in the user being granted the permission to perform an operation on a resource. A failed authorization will result in the denial of the same permission.