Before I explain Ideal Realism, it's important that I explain how exactly one should view philosophy.
Most people think that philosophy consists of reading "philosophy books." -- Authors of today and yesterday who explain their ideas in lengthy, convoluted snippets of thought mashed together between the pages of a paperback. Certainly, this is philosophy--but there is another, more relevent kind: The way a person lives their life. -- Everyone is a philosopher.
Idealism and Realism:
Some people's "life-philosophies" are idealistic, others are realistic. Religion is a philosophy as well. In America, our Judeo-Christian religion/philosophy teaches one to be fairly idealistic. God is at the basis of all, and all is good. Some of those in our western culture reject this viewpoint and claim instead that the world is just as it seems - a connection of cause and effect; random molecules ram into one another until life springs up. Give it a few million years, and you have us, humans.
(And then there are those people never ponder the question at all. "Why are we here? Why not?")
But when idealists and realists converse, they must have a common language and common tools with which to speak. Unfortunately, this is rarely the case.
Idealism: Religious and idealistic people will often speak of faith and their personal inner heart-felt feelings. "You just know," they say. Certainly, that's great for the idealist's peace of mind, but the person with whom they are speaking gains nothing from such an affirmation. Rather, the realist who hears this from the idealist will use such a statement as further evidence that idealism has no basis in fact or thought, only feeling.
Realism: Pure "realists," likewise, often speak of philosophy incorrectly. Rejecting the "sappy" idealism as hug-yourself time, they instead remain purely logic based. Life is random; love, an emotion born of genetics to entice us to procreation; beauty, a certain connection of synapses. What the realists forget, however, is that this overanalyzation of existence is just as hard for an idealist to accept as idealist talk is for the realist. Just as it would be foolish to answer a math test philosophically ("2+2... well, first we must discuss what it means to add and then understand the nature of 'two'"), it's foolish to be overly scientific about philosophy. How we live our lives has very little to do with what we know of logic and science (as much as we try to fool ourselves otherwise - more on this later).
One other note about being philosophical: We only discuss our personal "life-philosophy" with people we care about - people we respect. If someone came up to you in a bus station and told you their life philosophy, you probably wouldn't argue. If it were your close friend, spouse, child... you'd pay more attention; maybe even get into a late-night discussion or argue. By talking about your philosophy, you open yourself to another person and by doing so you often learn a few new things.