Initially both Pikachu and the Pokémon Clefairy were chosen to be lead characters for the franchise merchandising, with the latter as the primary mascot to make the early comic book series more "engaging". However with the production of the animated series, Pikachu was chosen as the primary mascot, in an attempt to appeal to female viewers and their mothers, and under the belief that the creature presented the image of a recognizable intimate pet for children. Its color was also a deciding factor, as yellow is a primary color and easier for children to recognize from a distance, and with consideration to the fact the only other competing yellow mascot at the time was Winnie-the-Pooh.
Essentially, it's cute, so they thought that girls would be drawn to Pokemon if the mascot was a cute one, because Pokemon is mostly about battling and the lead character is a boy.
It's also the "4th starter" because Ash has a Pikachu, and in the anime he got a Pikachu that was a left over, really. It's reflected in Pokemon Yellow, you can essentially recreate Ash' team, with Pikachu as your starter, Charmander, Squirtle and Bulbasuar being give to you, Pidgey and Caterpie available early on, Snorlax blocking your path to Diglett Cave, etc. etc.
What can I say? We're all suckers for cute rodent electric types, so much so that no one questions why Gen VI's Dedenne looks like a miniature Raichu.
Pikachu - wiki