Captain America is Steve Rogers — a scrawny Brooklyn kid from the 1940s who was transformed into a super-soldier by a secret government experiment. His real identity has been public knowledge since his first comic appearance in 1941, so there is no mystery here — the story is about how he became who he is.
Steve Rogers wanted to fight in World War II but was rejected by the military due to his frail health and numerous physical ailments. A secret program called Operation Rebirth recruited him as a test subject for an experimental serum called the Super Soldier Serum. The procedure worked — he became physically perfect, with enhanced strength, speed, endurance, and durability that put him at the peak of human capability. A Nazi spy assassinated Dr. Erskine (the scientist) immediately after the procedure, making Steve the only successful super-soldier.
Steve was issued an indestructible vibranium shield as his weapon and sent to fight in WWII. After the war, he was frozen in ice and thawed 70 years later in the modern Marvel Universe, where he became the moral center of the Avengers.
Pro tip: Steve Rogers is one of Marvel's few heroes whose power comes entirely from the serum — he has no suit, no tech, no gadgets. His strength comes from his character and conviction. That is why he is the leader.