One of the more emotional specials (in a field of surprisingly good ones; Why, Charlie Brown, Why? and What Have We Learned, Charlie Brown? are also good, over-looked ones), this is an adaptation of a run of the Peanuts comic strip that appeared in the 60's, concerning Linus and Lucy moving away.
Peanuts specials are best when confronting an adult situation with a child's perspective- something that is lacking in most of the holiday specials; this is a rare episode that deals with a child's situation from a child's perspective. While many adults experience the loss of friends when they move away, rarely is it as traumatic (or as common) as in childhood. Charlie Brown has to learn to deal with the loss of his best friend (and only friend that accepts Charlie Brown the way he is), Linus' security blanket doesn't help with the anxiety of having to make new friends, and Lucy realizes how much she loves what she's leaving behind- what she's complained about her whole life.
The show ends on an up note, of course; the original run of comic strips had Linus and Lucy moving back, due to the protestations of fans...
Satisfying for fans, and a situation almost any child can relate to.