In its simplest terms, a contract is nothing more than an offer, acceptance of the offer, and consideration. The buyer and seller may have two different ideas about who owns the copyright. Let's say as well that the web designer also intends to retain that ownership. The buyer, on the other hand, may be a small company looking for a web site for the first time, or they are looking to upgrade their current web site. The buyer may think that they own that great new graphic because they paid for the work.
Many business people get by without written agreements and never have a problem.
Others experience their first problems only after using written contracts. For others, the costs associated with drafting and negotiating formal contracts are prohibitive. For the rest of you, here are some contract basics. Negotiate all the terms up front. Get the messy stuff out of the way.