Time Power increases the speed in which schemes generate their money. The better your Time Power, the quicker the money collection bar fills up.
Only Dennis cards can increase Time Power: each unique Dennis card offers it's own bonus, and all of the bonuses stack.
Just owning a single level 1 Dennis card can give a small increase to Time Power.
You can also increase your Time Power by levelling up any Dennis card, which further increases the speed of schemes.
For example: levelling up Rock God Dennis from level 1 to level 3 increases Time Power from x1.25 to x3. This makes the Gas Crisis scheme collect faster, from 107.9s to 44.9s.