We commonly hear of weight trainers injuring their rotator cuff. A cuff tear is probably the most common injury to the shoulder obtained through lifting weights. The rotator cuff is what actually keeps your shoulder in place. It is also responsible for lifting and rotating your arm. The cuff is made up of four muscles(suprasinatus, infraspinatus, teres minor, subscapularis); each of them can be torn individually. When the cuff it torn it is typically torn where the cuff tendon attaches to the head of the humerus.
The most common for a weight lifter is a tear in the supraspinatus. The injury typically begins with the tendon starting to fray. This begins to weaken the area. Once it has been weakened, typically heavy weights will complete the tear.

The supraspinatus can either experience a partial thickness tear, where soft tissue becomes damaged but it is not completely severed, or a full thickness tear. In a full thickness tear the soft tissue is split in two pieces. When a full thickness tear occurs it renders the muscle useless. Often times the other muscles of the rotator cuff can make up for the torn one. The deltoid can also begin to be used for some additional motion. This is great for those who only tear one muscle but the load of the specific arm is now being accounted for by two or three muscles opposed to four.
Symptoms of a cuff tear are typically: pain while resting, pain lifting your arm straight from the side, or straight up, and substantial weakness in certain range of motion exercises.
A full thickness tear will not get better with time. The muscle retracts and has to be brought back to the footprint (anatomical attachment) with a suture anchor. It cannot do this on its own.
Partial thickness tears in younger healthy individuals can often repair themselves with scar tissue formation. This does not happen without resting the joint for 8-12 weeks. If the joint is continually stressed, a full thickness tear is inevitable.