**Core Concept**
The question is testing the relationship between pelvic floor muscles and urinary incontinence. The pelvic floor muscles, including the levator ani and coccygeus muscles, play a crucial role in maintaining urinary continence and supporting pelvic organs.

**Why the Correct Answer is Right**
The correct answer is related to the levator ani muscle, specifically the pubococcygeus (PC) muscle, which is part of the levator ani muscle group. Injury to this muscle can lead to pelvic organ prolapse, including cystocele (bladder prolapse), rectocele (rectum prolapse), and uterine prolapse. This occurs because the PC muscle helps to support the pelvic organs and maintain urinary continence by increasing urethral pressure and preventing involuntary leakage.

**Why Each Wrong Option is Incorrect**
* **Option A:** Injury to the external anal sphincter muscle can lead to fecal incontinence, but it is not directly related to urinary incontinence or pelvic organ prolapse.
* **Option B:** The obturator internus muscle is involved in hip and pelvic movement, but it is not directly related to urinary continence or pelvic organ support.
* **Option D:** The iliococcygeus muscle is another part of the levator ani muscle group, but injury to this muscle is less likely to cause urinary incontinence and pelvic organ prolapse compared to the pubococcygeus muscle.

**Clinical Pearl / High-Yield Fact**
The "3 Ps" of pelvic floor dysfunction are pelvic pain, pelvic organ prolapse, and pelvic floor dysfunction, including urinary incontinence. Understanding the relationship between these conditions is crucial for diagnosis and management.

**Correct Answer:** C.