。
In short, Sherlock is alive.
Literal
Essentially Sherlock [topic-は] is-alive-[explanatory-んだ].
生きている is 生きる ('live') in the ~ている form — 'to be alive / be living' (the ongoing state). Using 生きる without ~ている would describe the act of living, not the state. A dramatic revelation tone, helped by んだ.