Detective Pikachu is a clone of Pikachu that was put in the WaMachine. It is nearly like Pikachu, but instead is like a really good detective like Sherlock Holmes, drinks a lot of coffee, and looks like he's from real life or something.
He is Saitama's other disciple, and they actually fight bad guys together. Not that Saitama needs any more help, but because Detective Pikachu needs the training and fighting experience. Speaking of that, Detective Pikachu is actually a pretty good fighter, as well as an awesome detective.
As a detective, Detective Pikachu investigates all sorts of cases, while having a lot of fun and adventure at his job. The types of cases he would investigate are murders, crimes, cyber-crimes (like hacking), and other things. While he does enjoy being a detective, he also enjoys tap-dancing. Ikr, what a weird interest!