Autoattack means you weapon swings at your enemy, doing some dmg, specified by some tricky combat formulas that may be ancient or out of date. (search forum for Bruglirs combat formula if you want lovely math)
You will be doing autoattacks while casting instants, as the ability launch "cast" is 0 sec - but if you are channeling, you won't be autoattacking (say a DoK doing Rend Soul channel will not be autoattacking while doing the channel). Weapon speed is somewhat important, as it means how long the interval is between weapon swings - if its 2s, it means you swing weapon every 2 sec, if its 4s, it means your weapon swings every 4s - obviously smaller speed means it hits more often, but game compensates longer speed by making those hits usually hit harder (1 swing of greatswords vs multiple fast dagger stabs) - but as autoattack hits can proc dmg procs, often many small hits are preferable over big long swings. The DPS in the weapon is also important as IIRC, it influences the dmg of your autoattack (if and how much it influences your ability dmg, I cannot remember without rechecking formulas).
Procs trigger on all dmg hits, unless specified to be "on being hit" or otherwise. Procs that trigger "on hit" usually mean they trigger when you launch a hit, whether autoattack or ability - autoattack (AA) can proc your dmg/effect procs on your primary target, but some abilities that do AOE can in theory cause multiple procs to occurs, say you have gear that causes proc "enemies lose 100 toughness" - it can proc from AoE, so if you have 10% chance to trigger it and are hitting 10 people (aoe cap is 9 though), on average 1 of those 10 targets would be victim of said proc. Or maybe you get lucky and despite 10% proc chance 2-3 of your targets received the proc effect.
Dmg calculation is bit complex, don't remember exact formula from head (can be searched on forums if you really want to) - but for simple autoattack hit (abilities are bit different IIRC as they take scalers from mainstant + tree specialization somehow into account);
-your offensive stat (Strenght if you melee for example) + melee power (these 2 combined together into your offensive melee Damage stat)[Vanq +4% might be applied here, not really sure]
vs enemy mitigation from toughness, mitigation from possible absorb, mitigation from physical armor mitigation(vs offensive armor ignore/bypass)/resistances if facing magical dmg(vs possible offensive resistance bypass/ignore).
[this probably isn't the correct way of things, but search forum for Bruglir combat formula - it's more correct and more elegantly written elsewhere]
Crit is more or less just extra modifier to your dmg, normal crit would be 1.5xdmg, but most mdps have +50% crit dmg modifier tactics meaning its 2xnormal dmg. (if you checking autoattacks crits, there is some variance that I personally cannot explain as it is not 1.5 in that case) - but important thing to remember that dmg absorb happens before your ability is crit/noncrit happens - say you are doing 500 normal attack or possible 1000 crit, and enemy has 300 absorb shield up- from normal attack 300 would be absorbed and 200 landed, and from crit 300 would be wasted on absorb and last 200 would be critting at 2x ratio meaning 400 lands, making absorbs somewhat effective at mitigating critical dmg.
I haven't probably checked the formulas during this year so something above might be wrong, feel free to correct.
