A few words on the embryology of our sex organs (the science of our anatomical development before we are born): You probably never realized that the male and female genitals are remarkably similar. In the first few weeks of existence as an embryo, the external genitals are the same— consisting of a genital tubercle (a midline swelling), urogenital folds (two vertically-oriented folds of tissue below the genital tubercle), and labioscrotal folds (two vertically-oriented folds outside the urogenital folds). In the presence of testosterone (the male sex hormone), the genital tubercle becomes the penile shaft and head; the urogenital folds fuse and become the urethra and part of the penile shaft; and the labio-scrotal folds fuse and become the scrotum. In the female embryo, the absence of testosterone causes the genital tubercle to become the clitoris, the urogenital folds to become the inner lips (labia minora), and the labio-scrotal folds to become the outer lips (labia majora). Essentially then, the penis and the clitoris are the same structure, as are the scrotum and outer labia.
On a functional level, sexuality is a very complex event dependent upon a number of body systems, including the endocrine system (which produces sex hormones); the central and peripheral nervous systems (which provide nerve control); and the vascular system (which conducts blood flow). While all of these systems must function in a normal, coordinated fashion, a healthy sexual response is, at its physical essence, largely about adequate blood flow to the genital and pelvic area. Increased blood flow to the genitals from sexual stimulation is what is responsible for the erect penis. In a male, blood flow to the penis is analogous to air pressure in a tire: if there is not enough air, thereby causing the tire to be improperly inflated, the tire works less optimally.