You undoubtedly already pointed out that certain pens (not all) have a hole on the side (see picture).

This hole has its importance, without it your pen will not work!

Ink contained in the pen is locked up
in the body of your pen. When you
write with youe pen, inks diminish.
The volume of ink that was taken
away must be replaced by air. When
you empty a bottle of water, water is
progressively replaced by air. In the
case of your pen, ink are isolated
from outside the body of the pen,
therefore no air can enter inside your
pen.

When ink diminishes, air contained in
the pen is going to replace the volume of ink taken away. Therefore air will dilate. If air dilates he is going to want to come back to his initial state and therefore to inhale ink. If your ink are inhaled you cannot write any more. On the contrary if we make a hole in the body of the pen the ink volume taken away will be replaced with the same volume of air which will come outside. Air contained in the pen does not dilate and ink is not inhaled.