The gluteus maximus is the largest muscle in the human body by both mass and volume. Located in the buttock, it forms the bulk of the gluteal region and is the most superficial of the three gluteal muscles (gluteus maximus, medius, and minimus). Its primary functions are hip extension (straightening the hip joint when standing up from a seated position, climbing stairs, or sprinting) and external rotation of the thigh. It is essential for maintaining an upright posture and generating powerful movements of the lower body.
The other options, while large muscles, are not the largest:
The latissimus dorsi is the broadest muscle of the back (its name means "broadest of the back"). It covers a large surface area but has less overall mass than the gluteus maximus.
The quadriceps is a group of four muscles on the front of the thigh. While collectively powerful, the question asks about a single muscle, and individually none of the four quadriceps components exceeds the gluteus maximus in size.
The deltoid is the triangular muscle capping the shoulder. It is much smaller in mass than the gluteus maximus.