First, let's talk about recommending stuff based on your past behavior. One technique is called user-based collaborative filtering, and here's how it works:

1. The idea here is we build up a matrix of everything that every user has ever bought, or viewed, or rated, or whatever signal of interest that you want to base the system on. So basically, we end up with a row for every user in our system, and that row contains all the things they did that might indicate some sort of interest in a given product. So, picture a table, I have users for the rows, and each column is an item, okay? That might be a movie, a product, a web page, whatever; you can use this for many different things.
2. I then use that matrix to compute the similarity between different users. So, I basically treat each row of this as a vector and I can compute the similarity between each vector of users, based on their behavior.
3. Two users who liked mostly the same things would be very similar to each other and I can then sort this by those similarity scores. If I can find all the users similar to you based on their past behavior, I can then find the users most similar to me, and recommend stuff that they liked that I didn't look at yet.

Let's look at a real example, and it'll make a little bit more sense:

Let's say that this nice lady in the preceding image watched Star Wars and The Empire Strikes Back and she loved them both. So, we have a user vector, of this lady, giving a 5-star rating to Star Wars and The Empire Strikes Back.

Let's also say Mr. Edgy Mohawk Man comes along and he only watched Star Wars. That's the only thing he's seen, he doesn't know about The Empire Strikes Back yet, somehow, he lives in some strange universe where he doesn't know that there are actually many, many Star Wars movies, growing every year in fact.

We can of course say that this guy's actually similar to this other lady because they both enjoyed Star Wars a lot, so their similarity score is probably fairly good and we can say, okay, well, what has this lady enjoyed that he hasn't seen yet? And, The Empire Strikes Back is one, so we can then take that information that these two users are similar based on their enjoyment of Star Wars, find that this lady also liked The Empire Strikes Back, and then present that as a good recommendation for Mr. Edgy Mohawk Man.

We can then go ahead and recommend The Empire Strikes Back to him and he'll probably love it, because in my opinion, it's actually a better film! But I'm not going to get into geek wars with you here.