>>11088761I dunno if OP will understand this
My attempt at simplification feel free to correct/clarify.
Turing and Church showed that computation that can be expressed as a series of logical steps can be modelled by a Turing machine. Computational power is about how many steps does it take for a TM to perform your task. They showed that a Turing machine to compute a particular algorithm for a particular task can be encoded in a way that another Turing machine can be made to simulate your original one, albeit with some small overhead in the number of steps.
So you can built a universal Turing machine that can perform the tasks of all other TMs and use it as a reference point.
The steps-overhead for representing your algo on a universal TM is usually small compared to the other aspects affecting the #steps; such as the task itself, the algorithm/TM you design, and the length of your input.
Consider the difference for doing 'a*b' via 'a+a+...+a' (b number of times) or via long multiplication. The first method requires at least b steps so for very large inputs it can be very slow. Long multiplication is a far superior method for large numbers.
How much the number of steps scales with the increase in input size is an important problem, for example if the number of steps taken scales with exp(N) then you're fucked and you'll need a supercomputer to stand a chance.
There are certain problems for which all known algorithms scale badly like this for classical computers, but for quantum computers scale ok. So once you've built a good enough quantum computer you can solve problems that take too long with classical computers and we can solve stuff that humanity has literally never done before.
You can put temporal units to 'number of steps' by measuring how many steps your computer does in a second, obviously this depends on hardware so the fundamental Turing machine model is more useful.
