Serbia had had dreams of a southern-Slav state for a while. (Yugoslavia translates roughly to land of the Southern Slavs). The territory that is currently Serbia was part of the Ottoman empire until the late 19th century when the Ottomans were pushed out. The territory was still legally part of the Ottoman empire but was unofficially overseen by Austria-Hungary. This gave a feeling of pseudo-independence to the area. Early in the 20th century (1905?) Austria-Hungary decided to formally annex area. (They'll pulled some political hijinx to get Russia to say that they wouldn't intervene as Russia was pro-Slav.) Serbia was not happy about this and hence the "pissed off" feeling towards Austria-Hungary. Franz Ferdinand thought that if he could just go to the area and show "his people" that he was on their side that he could win them over. (He was quite out of touch with the actual sentiments of the people.) He was wrong, and Princip decided he'd prefer him dead.

This is obviously heavily paraphrased from my current reading of The Fall of the Dynasties. It's a fantastic book that I recommend if you're interested in the subject.