Mining Efficency

Mining consists of of trying to solve a maths problem involving the current block state and a random number. Everyone competes to find the right random number to use to solve the problem (the "difficulty" of the problem scales dynamically with the number of people competing via measuring how fast solutions are found). Once you've found it, it's pretty easy to check, but finding it requires many, many attempts.
It may require lots of computing power to do but it is extremely secure - it's very difficult to subvert (assuming no bugs etc).
It means people are creating new coins essentially from electricity - they're now primary producers, converting the simplest, most basic real-world resource directly into currency.

As to whether it becomes more or less efficient, as the value of a coin goes up, more people want to mine it (because they want the coin reward). People (generally) don't mine at a loss, so that balances the price of the coin against the price of the power used to create them.
That means the cost-efficiency at least stays relatively stable.