The brain is complicated. I did try to battle that in my post 'Breaking down the mind' (link below). But, it's true. To make it clear, this isn't biology. Its theory of knowledge (somewhat).
We think all the time, sometimes we know it, sometimes we don't. Sometimes we don't? Hmmm. What's that supposed to mean? If you started thinking of intuition right now, I'm getting better  at writing, if not, now would be a great time to start. I'm going to try and make you believe that intuition is an illusion. Our brain is biased towards 2 things. patterns, and things we desire, and/or believe in.
It's happened to us, we wake up in the morning feeling that it's going to rain and hours later it does. Several times, more often than not actually. There are two explanations I can put forward for this.
    1. Your brain is biased towards things you belive in, which holds true when it comes to making               memories, to your brain tends to remember the times that your 'intuition' worked rather than the           times that it didn't.
    2. Thoughts that you had that didn't amount to anything fade away quickly, as if we keep running           ccleaner (link below), and efficiently remove unnecessary data to free up disk space. All that's             left is thoughts that did amount to something i.e. where it did rain.
That would be intuition.

Our brain, has two systems, one fast and instinctive, for choices where speed is prime, and the second slow and thoughtful, for decisions that take processing.
2+2=?
 You probably answered instantly, as system 1 took over, first because this information is ready and you've answered this question before too, and second because you don't have anything at stake, so loss would not hit particularly hard.

But what about:
Should I take this offer?
What's 223568 + 66727?
Effect or affect?
 These questions would take longer to answer as the circumstances are opposite of the ones above.
If you want to read more on this, read the book 'Thinking fast and slow' by economist and nobel laureate Daniel Kahneman. (link below)

We think when we don't know that we're thinking. In the video 'the counterintuitive physics of riding a bike' minutephysics shows a great example of this phenomenon. Our brain, through years of experience automatically learns about classical mechanics and believe it or not, derives from its observations. We know how gravity does its thing. If you drop a ball, it falls and if you lean enough to get your center of gravity off of your body then you can fall over. And we also know, how we turn a bike. Do we? watch this video and continue right on. Click here

Did you see that! Your brain knew to turn to the other side! It thought about something subconsciously! you probably wouldn't know about this if someone asked you, even if you know how to ride a bike.

 But, then what is this subconsciousness! and doesn't it ask us before it does its thing? Check out these links, and as always, never stop asking questions.

subconsciousness?
www.youtube.com
The counterintuitive physics of turning a bike:
www.youtube.com
Thinking fast and slow:
www.amazon.in
ccleaner No, nobody paid for this, I just really like ccleaner.
www.piriform.com

So this was post 1 of 'How we think and learn' go chuck norris in that comment section if you like it, and keep 
a check for the next one. Peace.