What does anular tear mean? Diagnosis on my MRI spine. Need operation? Lots of pain!

Conservative . An annular tear only really affects the outermost portion of the disc. It can causes quite a bit of back pain, even some leg pain. Generally this pain subsides with conservative management: physical therapy, stretching, time, occasionally steroid injections. Mainly needs time to heal. Surgery is rarely indicated.
Not necessarily. A tear of the annulus of the intervertebral disc is a tear in the tough outer fibrous membrane, containing the nucleus pulposis or shock absorbing "gelatin like" substance. The need for surgery is determned by the symptoms and to some extent the pathology as seen on mri, ct scan etc. Usually relief occurs with steroids orally or as epidural, nerve root block etc. Speak with your spine specialist.
Annular tear. Annulus is fibrous ring of tissue surrounding a disc's jelly-like nucleus. Degeneration can cause tears extending from the pulp outward to the edge & let pulp material extrude (& possibly put pressure on nerves/spinal cord). Discuss the MRI findings with your doc/orthopod/neurologist to determine what course of tx is needed to give you relief.