I like to think of this problem in terms of entropy or relative concentration.
To undergo an intermolecular reaction you have to overcome the entropic penalty of bringing two molecules together. However, in an intramolecular reaction, the two reactive sites are already close to one another because they are tethered, so there isn't the same entropic penalty. (Although there still is an entropy component.)
You can also think of it this way: You know that things tend to react faster at higher concentration because there is a greater chance of the two reactive parts hitting one another that way. If you think of the concentration of the two reactive ends of a molecule undergoing an intramolecular reactiong, the two ends are always close and therefore have a high local concentration.