Weight training aims to build muscle by prompting two different types of hypertrophy: sarcoplasmic and myofibrillar. Sarcoplasmic hypertrophy leads to larger muscles and so is favored by bodybuilders more than myofibrillar hypertrophy, which builds athletic strength. Sarcoplasmic hypertrophy is triggered by increasing repetitions, whereas myofibrillar hypertrophy is triggered by lifting heavier weight. In either case, there is an increase in both size and strength of the muscles (compared to what happens if that same individual does not lift weights at all), however, the emphasis is different.
Intensive weight training causes micro-tears to the muscles being trained; this is generally known as microtrauma. These micro-tears in the muscle contribute to the soreness felt after exercise, called delayed onset muscle soreness (DOMS). It is the repair of these micro-traumas that results in muscle growth. Normally, this soreness becomes most apparent a day or two after a workout. However, as muscles become adapted to the exercises, soreness tends to decrease.