By Dr Ananya Mandal, MD. Celebrex (celecoxib) is a non-steroidal anti-inflammatory drug (NSAID) used to relieve pain, swelling and joint stiffness in conditions such as rheumatoid arthritis, osteoarthritis, ankylosing spondylitis and juvenile rheumatoid arthritis.y Dr Ananya Mandal, MD. Celebrex (celecoxib) is a non-steroidal anti-inflammatory drug (NSAID) used to relieve pain, swelling and joint stiffness in conditions such as rheumatoid arthritis, osteoarthritis, ankylosing spondylitis and juvenile rheumatoid arthritis.