Most dulcimers come with a doubled melody string, 2 strings tuned to the same note, and placed very close together. The idea here is to have the melody a bit louder than the other strings. They are and used as if they were one string. Some players like to separate the pair, tuning them to different notes. This allows 4 note chords, and also can allow the use of tunings which have no missing notes. This is used a lot by players who like to play swing and other styles of music that require more complex melodies and chords from outside the key in which the song is written. There are a number of tunings using this setup.
Some players use only a single melody string, either buying a 3 string dulcimer, or removing one of the paired strings. Often this is done to make it a bit easier to learn the instrument, though I don't think the difference is significant, if the string height was properly adjusted before purchase.
Like Rob, I have one dulcimer on which I have tried using several different string set ups. I did go so far as to add a 5th string to it, though, as Rob said, most dulcimers won't have enough space on the peg head to add another tuning machine. I managed to fit one in, but a dulcimer designed for 5 strings might have been a good idea. After all, we all want "just one more."
Some of this is due to players wanting to do things the 3 note tuning doesn't allow. My 5 string lets me do things a bit differently than my other dulcimer. Is it necessary? Not a bit. But we sometimes indulge our whims. Robs suggestions are good. They will allow you to experiment with a few set ups and playing styles without making expensive changes, or buying more dulcimers. Not that buying more is a bad thing, as long as you aren't raiding the kids piggy bank to do so. If there are specific styles of music you want to play, this may affect your decision. What do you have in mind?
Paul