Serendipity is one of the most beautiful words I know. It derives from an old Persian Fairy Tale, the The Three Princes of Serendip.
In the camel story, the Three Princes use trace clues to precisely identify a camel they have never seen (lame; blind in one eye; missing a tooth; carrying a pregnant maiden; bearing honey on one side and butter on the other). This result of abductive reasoning is not what is meant by serendipity (the discovery of something not sought). Because of their cleverness and sagacity, they are accused of stealing the camel and are about to be put to death by Bahram Gur. Suddenly and without anyone seeking him out, a traveler steps forward to say that he has just seen the missing camel wandering in the desert. Bahram spares the lives of the Three Princes, lavishes them with rich rewards and appoints them as advisers. These rewards are the unsought (serendipitous) results of their sagacious insights.
So, in fact it means: finding or discovering something fortunate, while actually looking for something totally different.
As most of us using search machines, browsing the Internet and looking for something in particular ending up with something different but very interesting. Serendipity gets more important due to the digital area we are going through.
But the more interesting thing is: many inventions are made, discoveries done etc. by serendipity: Read here more.