In left lower abdomen you have the sigmoid colon, which is also called the descending colon. So this is the reason why cancer of the colon in that area could produce pain; but constipation, ulcerative colitis, diverticulitis or irritable bowel syndrome could also cause pain in that region. In women ovarian cancer or ovarian cysts may produce pain in the region. Women can also get PID (pelvic inflammatory disease) from a Chlamydia or gonorrhea infection or a tubal pregnancy that needs to be diagnosed early to prevent a massive bleed when it ruptures.
Males have their share of problems: a testicular torsion is a painful condition that will have pain in the testicular area, but will also radiate into the lower left or right abdomen depending on what side it is on. Another typically male problem is an inguinal hernia. Due to the fact that in embryonic life the testicles descended through the inguinal canal, there is a certain weakness in the inguinal area where with heavy lifting the weak abdominal wall can rupture internally. If this happens on the left there will be a loop of the sigmoid colon attempting to escape the abdominal cavity and get stuck in the inguinal canal. You only have 4 to 6 hours to rescue the gut that is affected. A surgeon has to see the patient and move the sigmoid back into the abdominal cavity and surgically close the hole in the abdominal wall to prevent future problems. Unfortunately this often happens in older men when the connective tissue is weaker. In this age group this type of surgery has more complications than in a younger age. An ileus can happen with an inguinal hernia where the gut stops working. Sometimes an ileus develops when there had been previous abdominal surgery and a bowel loop (small bowel or large intestine) gets caught in adhesions (=scar tissue) from prior surgery. This is an acute emergency where you need to see a general surgeon.
A kidney stone passing from the left kidney into the bladder may cause labor-like pains while being transported there through rhythmic, spasmodic contractions of the ureter producing pain in the left abdomen. Crohn’s disease is another bowel disease of both the small and the large intestine that can cause pain wherever it is active including the left lower abdomen.