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"Unlike more deliberate and cautious magic-users, wizards are lightning rods for Arcane Power. An intense energy courses through them, and they direct it as though it were an extension of their own bodies. Wizards continually crackle with Arcane Power — it regenerates itself quickly, and so they can call upon their lesser abilities seemingly without end. They are only in danger of depleting their stores of energy when attempting a number of invocations at once. However, Arcane Power can ravage wizards’ bodies if its use is not carefully paced, so Wizards must endure a cooldown period before repeatedly casting certain potent spells. These spells — conjured meteors falling from the sky, torrents of force that shove multiple foes off their feet, or energy bubbles that halt the flow of time itself — are so powerful that they are worth the wait."— Game Guide(src)
Arcane Power is normally limited to 100, with Wizard-specific items being able to increase its maximum by up to +45 (+54 with Legendary items), plus additional up to +20 from Astral Presence and -20 from Energy Armor (can be +20 as well with Energy Tap rune). Paragon levels may grant +25 more Arcane Power.
It regenerates naturally at 10 per second rate, can be potentially increased by +4.5 from Arcanot, +1.4 from Kormac and +2.5 from Astral Presence skill. In addition, Wizard can have up to 8 (14 with The Oculus) Arcane Power restored per critical hit, multiplied by Proc Coefficient of each particular spell. The Shame of Delsere makes Signature Spells restore 9-12 Arcane Power on cast.
Certain skill runes also recover Arcane Power on hit. Combined with skills like Prodigy, it allows a near-infinite Arcane Power with the proper build and gear. Some Arcane Power-independent builds exist as well.