Archtops and Hollow Body Guitars
From early carved archtops to laminated archtops to solid body guitar was mostly an evolution in the quest for more volume. See the History of the Solid Body Electric Guitar.
The archtop design was meant to increase the power and quality of tone an instrument was capable of in the days of acoustic instruments. It is effective in increasing volume and projection. Archtops were widely adopted before amplification was available.
The early acoustic archtop guitar was loud enough for small spaces and smaller performances. Once the pickup and amplifier were available many guitar makers like Gibson just attached pickups to the existing archtops. As guitars were electrified and were played at higher volumes, feedback became a problem that needed to be solved. Eventually the solid body guitar build from a hunk of wood routed for pickups solved this feedback issue. No more danger of howling when the volume was raised and the guitar was close to an amplifier. In the case of archtops or hollow body guitars that does not tell the entire story.

Ted Nugent with Gibson Byrdland
Intonation is what keeps your guitar in tune when fretting notes. Easy with any tuner, be it clip on, pedal or good ears to get your guitar’s open strings set to standard tuning. But as you fret up the neck you want your guitar to stay as close to in tune as possible. If your guitar sounds out of tune when playing some chords or when playing fretted notes up at the higher frets your guitar’s intonation needs setting. Depending on what type of bridge, strings your guitar has plays a big factor in this setting. 

