The wikipedia article goes on, "customers typically have an abstract idea of what they want as an end result, but not what software should do." My experience in systems administration is that customers may have an idea of what they want as an end result, but they may not know what problem they are solving and often present their idea in the form of a solution.
To describe this with an example, let's say you have a small team of sysadmins who are familiar with mysql and your group supports a few mysql deployments in your company.
A customer says, "I need postgresql installed." This is a request for action, not a description of the problem. You are only given the solution that the customer believes will bring about their desired end result. Do you simply install postgresql for them, or do you ask why they need it? If you already have a well-supported mysql deployment, you should be asking why you need to support another database.
Ask about the problem they need solved. Get details. Why does he or she need postgres? Can the existing mysql deployment and knowledge be used instead? Most of the time customers who simply ask for actions, "please implement this solution," often are unaware of existing, similar options already available. It's also possible that this customer is trying to solve a problem that doesn't exist, doesn't affect your company, or isn't feasible to solve completely.
If you get requirements, you might find they are simply "I need a database that speaks SQL." Alternately, you might find that the requirements include "I need to run this 3rd party tool which requires postgres." Dig deeper. What does this tool do? Can it's features be provided by another tool that doesn't require burdening your team with additional products to support? Is the problem the customer wants to solve even in the scope of your team?
In addition to getting the necessary information about the problem, you should also make sure you are given other constraints and parameters. Is there a deadline? What is the scope of the problem, who is affected, etc? What is the priority?
Let's examine another common situation. Another customer says, "I need apache on serverfoo restarted." Again, you should ask for a description of the problem. What are the symptoms the customer is observing? Restarting apache is an action that could bring about a solution, but what are you solving? What is broken? What if a customer reports "mail is down?" What does "mail is down" mean? What are the symptoms being observed?
When digging for a description of the problem from your customer(s), be careful to not offend the customer. It's easy to dismiss the customer as an idiot if you the information you are given doesn't make sense or doesn't help you fix a problem. This issue can easily occur when a non-domain-expert interacts with a domain expert. Remember that perspective is reality, and that "mail is down" makes total sense to your customer but is confusing to you. Make sure your fellow sysadmins follow the advice in this paragraph, too.
Asking for requirements can be a tool to help push back on bad ideas. Sometimes a management hammer comes down from above and says you must implement something that you disagree with or don't understand. Being a domain expert, you might be disagreeing or lacking understanding because the request doesn't make sense. Ask for requirements! Sometimes ideas manifest themselves into requests (or mandates) without the idea being actually thought out.
Lastly, always remember you can say, "no." Not every idea is a good one. Bad ideas can come with urgency. Be understanding of any urgency from your customers, but remember that you have the most information about what makes a change bad. Otherwise, why would they be asking you or your team to do it? Be aware of things people will say to convince you to do something even though you can show it is incorrect, such as "the CEO said we have to do this." Facts are your ally, so use facts to show why a proposal is wrong, why a request doesn't make sense, or why a set of requirements are impossible to fulfill.