As the name suggests, Signature Moves are the moves that can be learned by only one Pokemon’s species (this includes its evolutions). Most of the time, it follows this path; Signature Moves that can be learned by the three species of starters are the only exception. Before the Sinnoh region came out, many species of Pokemon had their own unique Signature Move. When Diamond and Pearl came out, some of those Pokemon inherited these Signature Moves, no longer making them exist. Many know Signature Moves mainly because of legendary Pokemon. Recently, Zekrom and Reshiram have each had a signature move. Fusion Bolt correlates to Zekrom’s Dragon/Electric-type, and Fusion Flare represents Reshiram’s Dragon/Fire-type. Signature Moves are actually more common than I thought.
Before Sinnoh, at least a hundred Pokemon had its own special move. Meowth’s Signature Move was Pay Day, since it had a liking for shiny objects. The Porygon series (Porygon, Porygon2, and Porygon-Z) have Conversion and Conversion 2 as their Signature Moves, since they are the only computer Pokemon in this game. Pichu has Volt Tackle, a move we see frequently used by Pikachu in the new Pokemon TV series. Many the moves we see today are no longer bound to one Pokemon alone, although some exceptions to the case have been made. Smeargle, the painting dog, keeps its move Sketch (and learns it again every 10-11 levels). Delibird, the generous food-giving Pokemon, still has its unique move, Present. A possible (and very likely) reason many moves are no longer deemed one-of-a-kind is that the creators did not want the players to get mixed up with moves.
However, new moves are constantly being introduced to the game, which can be learned by a variety of Pokemon from the older generations. Each move has its own perk to it. For example, if you use Pay Day, you will always get a small amount of Poke Dollars, regardless if you are fighting a wild Pokemon. One can also say that Signature Abilities exist, which sometimes coincide with Signature Moves.
For example, Zekrom and Reshiram’s Teravolt and Turboblaze make a great combination with Fusion Bolt/Flare, seeing as if the Pokemon’s ability is Sturdy, it can be knocked out in one hit. But what exactly makes a Signature move, well, signature? Signature moves conform to the Pokemon in its own way. Who else but a painting dog could learn Sketch, and why would any other Pokemon except Meowth have Pay Day? In other words, they fit naturally to the Pokemon, and if others could learn it, each Pokemon would not be original. Thus, Signature Moves are quite a nice touch to the game, and can range from being an effective status move to being a power-packed physical move. It makes Pokemon exciting, unpredictable, and addicting, no matter what one’s age is.