Making a skill Legendary can be both a great thing and a terrible thing. This allows you to level the skill up all over again, thereby gaining XP for the skill ranks just as you did to begin with. Third, a Skyrim dragon glyph appears over that skill in your Talent screen. Second, it reduces your rank in that skill to 15.
First of all, it refunds you all the talent points you put into learning talents for that skill, taking away all of those talents.
Once a skill reaches level 100, you can use the Talent screen to choose to make that skill Legendary. Despite the nomenclature implying that these skills are somehow superior to the original skills or represent an even further level of capability, they are actually exactly the opposite. One of the introductions in later versions of Skyrim was Legendary Skills. Because of this, in the original iteration of the game, there was a limit to how many levels a character could gain: once all skills are at level 100, the character can gain no more experience and thus no more levels. In the game of Skyrim, your character gains levels through use of their skills- each time a skill gains a rank, the character gains experience towards improving their character level.