If you are facing something that will be difficult to handle, you have a problem on your hands. A problem is a roadblock in a situation, something that sets up a conflict and forces you to find a resolution.
The meaning of the Greek word próblēma meant "to put forth," which is different from the meaning of problem today, but it reminds you that any problem becomes easier to solve once you have defined it. A math problem is easier once you have the numbers in front of you: that's why word problems can be so difficult. Problem can also be an adjective in rare cases. Once you were a problem child, but now you spend your time listening to everyone else's problems.