Why are problems in P easy and other problems not Problems in $P$ have polynomial time algorithms. Problems in e.g. $NP-complete$ are only solvable in "probably exponential time" (Shen Lin's PET).

Problems in $P$ are considered easy while others (most likely) are not.

What does easy mean?
I've always thought of hard and easy this way:

Our computing power grows exponentially over time. A problem is called easy if we can solve exponentially more instances of it (in reasonable time) after each time unit. A problem is hard if we can only solve polynomialy more instances of it after each time unit.

I'm well aware of complexity analysis, the definitions and their meaning. I'm trying to propose a reasonable, intuitive and easy to understand explanation of hard and easy. Would the explaination above explain it correctly and would someone who never heard of the subject understand it?
Your definition of "easy" doesn't make much sense. What exactly does "solving more instances at each time unit" mean?

Usually our notion of hardness refers to our ability to "solve" one instance. More formally, let $T(n)$ be the amount of operations required (proportional to time) for inputs of size $n$, then by "hard" we usually mean that $T$ grows too fast.

As for why polynomial $T(n)$ is considered easy, see this question.