A filter is a small threaded cell which screws onto the base of an eyepiece. They serve a wide array of purposes such as a moon filter which darkens the bright surface for study—to something as exotic as a nebula filter which allows only certain bandwidths of light to pass through. Some of the most common filters you find will come in colors labeled by wratten numbers. These help to see better contrast in some planetary details.
While no filters are essential to practice astronomy, those who wish to make a hobby of studying the Moon will greatly appreciate a moon or polarizing filter. For those interested in the planets, a simple set of the four basic wratten colors are fine. If you live in a highly light polluted area, there are special filters which neutralize unwanted bandwidths of light—just as there are specialty filters that improve the contrast of nebulas—and specific wratten colors which improve photography.
Remember that these are not necessities, and you just might find if you wish to add them to your kit that filters can be fairly inexpensive when purchased as a set.