Idealism is a doctrine and metaphysical theory which supposes that there is a difference between appearance and reality. Some philosophers think idealism began with Plato's Ideal Forms (abstract notions and ideas). Plato's Ideal Forms were abstract, immaterial, the absolute truth. Therefore, these abstract forms were notably different from how we empirically/physically experience the world.
However, more philosophers tend to agree that idealism begins with Descartes who famously said, "I think, therefore I am." Thus, idealism is also a philosophy that our apprehension of reality (as appearance or 'actual reality') has to do with how our minds apprehend (think and experience) things in the world.
Immanuel Kant described the "thing in itself" (noumena) and things we experience ("phenomena"). Thus, there are objective things, ideas, and notions that we can not know or can only apprehend by pure reason; those things are noumena. And, there are things we apprehend empirically, with our senses; these things are phenomena. Kant argued for a transcendental idealism: we see representations of things - the things themselves in their actuality are beyond our empirical perspective. In other words, things as they actually are transcend sense experience. This just again underscores how we apprehend the world with our minds and senses, and this illustrates a difference between the experience of things as they appear and things as they really are. In Critique of Pure Reason, Kant writes:
. . . appearances are to be regarded as being, one and all, representations only, not things-in-themselves, and that time and space are therefore only sensible forms of our intuition, not determinations given as existing by themselves, nor conditions of objects viewed as things-in-themselves.
So, idealism supposes a distinction between actual reality and the way reality appears to us (the way we mentally and physically experience reality). Idealism is the description of this dichotomy and the philosophy of negotiating between the two worlds: appearance and 'actual' reality. This negotiation has everything to do with our minds, how we experience/think things and how we consciously apprehend things. The inevitable conclusion is that we apprehend the world via our minds. Whether or not that which we apprehend is 'actual reality' or "things-in-themselves" is up to the person or philosopher.
One problem with idealism is the idea of the objective, things-in-themselves, things we can not know with our own minds. If we can not know them, how do we know they exist? (This argument also leads to questions of spirituality.) One counter to the argument is that our senses are fallible and therefore, by that fact, we can not know things as they are because our senses could be flawed or distorted.
Different variations on idealism suggest different ways of solving the philosophical issues inherent in idealism; namely, the difference between appearance and reality, and the implications of the theory that reality (or the appearance of it) is, for us, something we mentally apprehend and/or mentally construct.