What do the numbers after skills indicate?

To elaborate on GinWolfe's answer:

The number doesn't indicate the damage of a skill. If that were the case, skills with 40+ would instantly defeat most opponents. Instead, this number indicates it's power level, which direct influences damage.

All pokemon games use the same principle of power, although I cannot confirm that it follows the exact same mechanics for calculating damage. For more information on power in previous pokemon games, check http://bulbapedia.bulbagarden.net/wiki/Power.

As GinWolfe already explained, the bars indicate when the second (special) move can be activated. Stronger moves generally have longer bars, requiring the player to charge it up (by attacking with the pokemon's normal move, like Tackle or Quick Attack) for longer period of time before it can be used. Multiple smaller bars simply means that once the first bar is filled, the second bar starts to fill so you can use your special skill multiple times in succession for each filled bar. These special moves can be activated by either pressing and holding on the enemy or by tapping one of the filled bars in the top left.

Source: personal experience

The skill combinations are battle moves. I've only been playing for a couple of days, but the numbers appear to be how much damage each single attack will do. (specifically, when you're in a Gym battle).

Your first Pidgey will do the most damage in combat. The final one will do the least.

The numbers represent the strength. The charging bars mean you have enough energy for your special attack (the second one, with the blue bars next to it.) Tap and hold while in battle to use the special attack.