**Aid Grades Explained: (but this is just like, my opinion man... )
The first thing to point out is the difference between the "A" ratings, and the "C" ratings. Essentially the difficulty associated with the numbers is the same. Difficulty in a simple description almost directly translates just to how scary it is. The difference in "A" or Aid ratings, and "C" or Clean ratings is the use of a hammer. Aid climbing is sort of a scrappy battle with the rock, the climber uses any technique known to him/her to get to the top. If there is a crack, chances are it is climbable with some shenaniganery of smashing different types of metal into said crack. Clean aid climbing is when a climber is still aid climbing and uses most of the same techniques, but does not use a hammer and therefore is less likely to damage the rock. It has become popular to try and climb as clean as possible because advancements in climbing technology promote it, and the evolving nature of climbing ethics. When a climber manages to climb the entire pitch without the use of a hammer it gets the "C" grade which is typically more difficult then the "A" grade.
A0: Most likely just a bolt ladder. This can probably be done without aid ladders. Consult local Beta if you need ladders.
A1: This is as easy as it gets outside bolt ladders. I am still always surprised how often I find myself half way up an A1 pitch and am saying to myself "I am so scared I want to cry and go home right now please..." But the hypothetical definition of this grade is that every single gear placement is strong enough to hold a fall. In reality though... maybe I need to practice placing gear or something because that doesn't always seem to be the case.
A2: This grade along with probably all of them, seems to have a very loose definition. But techinically you should expect mostly good gear, with occasional "body weight only" movements. This means that you might be forced to place a piece of climbing equipment that can only hold your weight in order to get up higher to make your next movement, and if you fall, which would be induced by a "less than body weight" placement, it will come out and you will continue falling until you reach a piece of gear that is solid. Typically A2 will not have a series of more then a couple "body weight only" placements.
A3: Starting to get even more scary. Many more sections of "body weight only" placements. Several in a row will be a common occurrence. But there is usually enough good gear on the pitch to keep the climber from being seriously injured in the event of a fall. Upon falling however, the climber can expect the infamous "zipper" phenomena, and perhaps even a chance to wave at the belayer as he/she goes screaming past the belay station on the way down. Examples of gear are bird beaks placed in very thin seams, or extended sections of hooks on small edges. The Clean grade "C3" will use a lot of offset cams in wonky and poor positions, or a lot of hand placed bird beaks and very small brassies and wires.
A4: I can not speak from personal experience on this grade, and I am not really sure if my aid climbing career will lead me here. Maybe some day if I run out of A3 walls... but for the moment I am content with "safe" aid climbing. Allegedly A4 will consist of even more "body weight only" placements to the extent that the majority of the pitch is comprised of them. A climber might get 1 or 2 pieces of gear in throughout the entire pitch that would stop a fall.
A5: Dangerous. You can scour youtube on your free time for the angry climber ranting about this grade. But my opinion is that A5 simply means that the entire pitch is body weight only, and a fall could mean serious, potentially fatal results.
A6: Hypothetical, and extremely dangerous. Even the anchor is "Body weight only", so if the climber falls, it would mean everything pulls out including the anchor and the climber or climbers continue to fall to whatever point physics deems it necessary that they stop.
C1 - C5: See the above descriptions, but apply without the use of a hammer.