"Make everything as simple as possible, but not simpler."
Within a context every object or process has a given amount of complexity. As Einstein said there is a base level of complexity that cannot be circumvented, but there are at least two types of complexity: inherent and artificial. There are many other names for these and many other ways to decompose complexity into subparts, but this simple breakdown clarifies a simple property of complexity, that is that under specific circumstances many complex things can be made simpler.
Simplification can occur for many reasons, but most commonly it is from removing artificial complexity. That is, the complexity that is piled on top for reasons like misunderstandings, short-cuts, disorganization, self interest and lack of understanding. Note that all of these are directly attributable to human intelligence, and with that we quite easy define 'inherent' complexity as the lower limit that is bounded by our physical world in the sense that Einstein really meant in his quote. Also note that I started the first sentence referring to context. By this I actually mean a combination of spacial and temporal context. Thus, things can get simpler because we have learned more about them over time or because we are choosing to tighten the boundaries of the problem down to avoid issues within the larger context. The latter however can be problematic if done under the wrong conditions.
For reducing complexity there is also the possibility of simplification by encapsulation, that is some part of the whole is hidden within a black box. The context within the box is obviously simpler, but the box itself adds something to the larger complexity. This works to some degree, but it can only be piled so high before it itself becomes too complex.
Often people attempt to simplify by reducing context, essentially "wearing blinders", but they don't follow through with the encapsulation. In that case, it is extremely unlikely that any underlying changes will actually simply things, instead they spawn off unexpected side effects which themselves are just added artificial complexity. This often goes by the name 'over simplifying' but it's a misnomer in that while the change within the context may be describable as a 'simplification' it isn't really.
Within this description we can also add abstraction as a means of simplifying stuff. In general it's really just a larger pattern or relationship manifested over a larger space of objects or processes, but it's ability to help comes from the fact that it organizes things underneath. Organization and sometimes categorization relate similar things together by properties, so exploiting these relations reduces the complexity of dealing with the individual parts. Abstraction thought has it limits in that it acts much like a bell curve. Some abstraction reduces complexity, increasing to a maximum point, then falling off again because the abstractions are too general to be applied for organization. Still a powerful abstraction, at a maximal point, can cut complexity by orders of magnitude, which is way more powerful than any other technique for controlling complexity. It's not free however in that considerable fewer people can deal with or understand strong abstractions. That leaves them subject to being misunderstood and thus becoming a generator of artificial complexity.
There are many ways to reduce or control complexity, but there are many more ways for people to introduce artificial complexity. It's this imbalance that is driving our modern age to the brink of serious trouble. So often people cry "simplification" while actually making things worse, and it isn't helped by living in an age where ability to spin the facts is valued far more than the ability to get things done well. Quantity and hype constantly trump quality and achievement.