"Loose lips sink ships." (Wikipedia)
Hackers use exposed information and feedback from their actions to their benefit. They probe and research systems using techniques such as footprinting, enumeration, and fingerprinting. Knowing information such as server attributes, configurations, or software versions can be helpful in finding and exploiting system vulnerabilities. It is similar to a safe cracker knowing the brand and model of the safe they are trying to crack. The attacker could know specific weaknesses or even zero-day exploits. Having more information helps to narrow the field of exploits and to focus their efforts.
Security through obscurity means do not report any more information than is absolutely necessary. Be stingy about what information is given out. Everything could be a clue, including interface feedback, form structure, or URLs. Servers should not report software versions (often these are included in responses headers).
The classic example is:
"The username was found, but the password is incorrect."
This information would allow an attacker to enter an arbitrary username into a login page and determine if there is an account present for that username. Given enough time, the attacker could build a complete list of active usernames. This process is called "enumeration". With a valid username, an attacker could then begin the process of determining the correct password to match that username (possibly using brute force or dictionary attacks).
However, the principle of security through obscurity is often misapplied. Developers sometimes believe that they are increasing by obscuring features. For example, they might hide an admin area with a URL like "somesite.com/xyzxyz/admin.php". Or they might use unexpected variable names. Making features or code deceptive or obscure does very little to increase security. In fact, making the code less clear and simple often causes bugs which make the system less secure.
Limit exposed information, but realize that deception offers little additional security.