Just because a website looks modern and has an updated look and feel, doesn't mean the information is accurate. Not all things in pretty packages are what they seem.
Currency refers to when the information was posted or published. It is also important to look at the entire website's timeliness. If it has remained dormant for some time, it may be a warning that the website is no longer being maintained.
Some Questions to Ask
How important is currency? That really depends on your topic and discipline. Sciences and medicine change rapidly and unless you are doing a historical piece on those topics, you are going to want to most current information available. If you are working with history or literature, it's quite possible that the currency is not very important. Use your best judgement and don't be afraid to ask a librarian or your instructor.