The word serendipity means a happy accident; something, usually pleasant, that you come across while looking for or doing something else. It's very hard to translate it, and didn't develop in the way of most modern words, eg gradually evolving from a particular root. Instead, it seems to have been made up by Horace Walpole (son of British Prime Minister Robert Walpole) in the 18th century. He used the term in 1754 in a letter to a friend, and explained that he had got the idea from a story in The Arabian Nights, called 'The Three Princes of Serendip', who often found pleasant or interesting things that they had not been looking for.
Serendip is an old Persian name for Sri Lanka, or if you trace it back to its Sanskrit origins it means 'golden island'.
A sentence might be, for example if you take your friends to a new place (say a restaurant) and they ask how you found it. You could say 'I wasn't looking for a restaurant, it was pure serendipity. In fact I was just looking through the paper and I saw an ad for this place.'