1890. That's right. The Steampunkolithic age! It used compressed gas bags to augment the users movements. in 1917 Leslie C. Kelley invented and patented the Pedomotor. STEAM POWERED! You wore a stem device on your back and it helped you run through pulling on artificial ligaments!
Of course the ability to power such things, well, sucked! The first true exo suit was built by GE in 1960. It was supposed to let the user lift loads up to 1500 lbs. Just like Sigourney Weaver in 'Aliens' in the loading bay. the issue here is when activated it would make such violent movements, it was never used with a person actually inside.
What do we like about the powered exo-skeleton? Movies! Anime! Giant fighting robots and ass-kicking! This was awesome. In fictional literature, Jules Verne wrote in 1880 'The steam house' about a giant steam powered piloted elephant. The idea is full of great.
E.E. Smith wrote about powered armor in 'the lensman' series starting in 1937. At first magazine published but then bookified in 1940.
After that Robert Heinlein wrote Starship Troopers, making the military power armor such a great thing for everyone to enjoy. Eve since then it's been used to kill aliens! and kill more aliens! and kill invaders...who are aliens! In one instance they were used to fight for sport but we wont talk about 'Robot Jox'. It was a good idea made into a horrible sad idea.
Military wise this is what they're trying to do. but honestly the real mecha will be disabled soldiers gaining mobility again. there is alot of work on this and it's very promising. But giant fighting machines? We are probably a ways off. No Pacific rim yet!