Why was the submarine invented?

Answer 1

Because it was needed for war.

Additional answer

Although the above may be correct, I think it's highly probable that it was invented simply because some people felt a desire to make this sort of thing work, without there necessarily being a reason for it at the time. Military uses may only have been thought of much later.
Originally, U-boats were built for Russia during their war with Japan in 1904 (Russo-Japanese War 1904-1905). After the war, the Germans took one of those export models, modified it, and commissioned U1 into their navy in 1906.
The first group of German submarines were built to be sold to Russia during the Russo-Japanese War in 1904. The German Navy's first U1 was taken from that group and commissioned in 1906.
for owls to see underwater your welcome!

Ans 2 - As with many things, war was the cause the submarine was invented for. The first ones were built to place bombs on or under the hulls of enemy ships before the US Civil War. It would be almost 50 years till the first practical torpedoes were used.