Why did Leonardo paint this?

Because his employer requested he do so. Leonardo worked for Ludovico Sforza, Duke of Milan, for nearly eighteen years (1482-99). The Duke decided he wanted this particular religious scene painted and Leonardo, who was not stupid, decided painting it made perfect financial sense.

How big is it?

It's huge, really - 460 x 880 cm (15 x 29 feet). It covers an entire large wall, very unlike reproductions sized to hang neatly behind one's sofa.

Where is it?

The original mural is on a wall of the refectory (dining hall) in the Convent of Santa Maria delle Grazie in Milan, Italy.