How come some cyclists lean forward at a 45 - 60 degree angle and I don't? I just wanted to ask how come some cyclists when they ride they lean forward, with their arms straight, resemble a 45 to 60 degree angle (which looks cool by the way).

I have a hybrid bike and I wish I could get that look and it seems to be more efficient because some of the weight looks to be shifted in the front wheel compared with cycling on a straight back (90-80 degrees angle).

Is it the distance between the seat and the handlebars? Is that the reason they have to bend their body? Or is it something else?
To complement Neil Fein's answer, the rider's position is almost entirely controlled (given a particular rider) by the geometry of the bike.

Compare the following bikes. In the first image of a hybrid bike, the saddle is slightly below the handlebars. In the second image depicting a road racing bike, the saddle is well above it, forcing the rider to lean farther over to reach the lower handlebar position. In the third image of a time trial bike, the seat height and handlebar height have remained relatively unchanged, but the seatpost is at a much steeper angle and the intended grip brings the arms much further forward, forcing an even more horizontal position in order to put the hands on the bars.





Now look at the riders in this next series of images to better see the difference.


(source: bicycledutch.wordpress.com)


(source: www.flickr.com)


(source: bikesportmichigan.com)