Depending on what definition of "strongest" is used, many different muscles in the human body can be characterized as being the "strongest."
In ordinary parlance, muscular "strength" usually refers to the ability to exert a force on an external object—for example, lifting a weight. By this definition, the masseter or jaw muscle is the strongest. The 1992 Guinness Book of Records records the achievement of a bite strength of 975 lbf (4337 N) for two seconds. What distinguishes the masseter is not anything special about the muscle itself, but its advantage in working against a much shorter lever arm than other muscles.
If "strength" refers to the force exerted by the muscle itself, e.g. on the place where it inserts into a bone, then the strongest muscles are those with the largest cross-sectional area at their belly. This is because the tension exerted by an individual skeletal (striated) muscle fiber does not vary much, either from muscle to muscle, or with length. Each fiber can exert a force on the order of 0.3 micronewtons. By this definition, the strongest muscle of the body is usually said to be the Quadriceps femoris or the Gluteus maximus.
Again taking strength to mean only "force" (in the physicist's sense, and as contrasted with "energy" or "power"), then a shorter muscle will be stronger "pound for pound" (i.e. by weight) than a longer muscle. The uterus may be the strongest muscle by weight in the human body. At the time when an infant is delivered, the human uterus weighs about 40 oz (1.1 kg). During childbirth, the uterus exerts 25 to 100 lbf (100 to 400 N) of downward force with each contraction.
The external muscles of the eye are conspicuously large and strong in relation to the small size and weight of the eyeball. It is frequently said that they are "the strongest muscles for the job they have to do" and are sometimes claimed to be "100 times stronger than they need to be." Eye movements, however, are and probably "need" to be exceptionally fast.
The unexplained statement that "the tongue is the strongest muscle in the body" appears frequently in lists of surprising facts, but it is difficult to find any definition of "strength" that would make this statement true. Note that technically the tongue consists of sixteen muscles, not one. The tongue may possibly be the strongest muscle at birth.
The heart has a claim to being the muscle that performs the largest quantity of physical work in the course of a lifetime. Estimates of the power output of the human heart range from 1 to 5 watts. This is much less than the maximum power output of other muscles; for example, the quadriceps can produce over 100 watts, but only for a few minutes. The heart does its work continuously over an entire lifetime without pause, and thus can "outwork" other muscles. An output of one watt continuously for seventy years yields a total work output of 2 to 3 ×109 joules.