You learn about it when studying for the Tech exam, but it's really not until you hook up that first antenna and find no one can hear you that you truly begin to understand the importance of SWR (or standing wave ratio). Of course, that doesn't mean you understand it, just that it IS important.
Sometimes it seems that SWR is one of the most mysterious creatures in the world of Amateur Radio. You can even hear on-air discussion of guys bragging about and comparing their SWR numbers as if it were a contest. There seems to be a relentless drive to achieve the most coveted 1:1 SWR at any cost. But why? This article (in PDF format from the ARRL) is written to help explain what SWR actually is, what makes it bad and when to worry about it.
Understanding SWR by Example