Hatsune Miku is a japanese computer program. The technology is called Vocaloid (=vocal android). That means, songs sung by her are made with the computer. A seiyuu (synchron speaker) 'lent Miku her voice'. As the user of the program ('Producer') you can make her sing everything you want - in Japanese. Other languages sound rather crappy, or at least like sung by someone with a japanese accent - depends on the producer.
Miku is often used (and designed) for pop songs, but there are also a bunch of horror and/or suicide songs by her on YouTube. She's the most known Vocaloid (but NOT the first!).
Note: Since it's Japanese, Miku is the given name and Hatsune the family name.