A stick pen is a kind of ballpoint pen designed for the primary purpose of being extremely inexpensive. Using a thick oil-based ink, they tend to write unevenly, requiring significant pressure (compared to other pens) to make a consistent mark on the page; even with consistent pressure, they tend to stick, a possible genesis of the term.
Stick pens are ubiquitous in modern life, as they are given away as promotional goodies by many companies, they are purchased in bulk by most workplaces for employee use, and many retail outlets supply them to customers for check-writing and credit slip signing. Stick pen theft, however, is rampant in this final situation, so most establishments go to extreme measures to handle this threat. The thievery of stick pens must be truly obscene, or such establishments wouldn't go to such trouble to protect $0.05 of merchandise.
The most reasonable of these approaches is to adhere extremely large stickers to the back of the pen, making them difficult to pocket. More common, however, is the purchase of a highly specailized pen on a chain, theoretically permanently affixed to the desk. In practice, the chain gets in the way, the pens tend to write poorly, and it seems astonishing that the cost of a chain pen is actually less than the cost of all the stick pens it prevents the larceny of.
As a nearly-disposable writing implement, the stick pen is a symbol of modern society: one of the most important inventions in human history, writing, is simply taken for granted as such a basic thing that its tools are among the cheapest commercial products available, a demonstration of how the most important objects in a society have the least attention paid them.