Honestly, it's very self explanatory. Weapon attack is the attack value of the weapon and if it says magic damage then it effects spells rather than physical attacks. Auto-attack is damage that your auto-attack does and delay is the time between auto-attacks. Very basic.

When it comes to BRD and MCH weapons being lower damage, that is slightly more involved. To put it simply, the devs believe that BRDs (there were no MCHs when this change was made) are able to output damage while being more mobile and offering more raid utility than other jobs made them a bit too good. As a trade off they lowered their weapon damage to balance them out.