A pair of star=crossed lovers take their life,
Whose misadventured piteous overthrows
Do with their death bury their parents" strife. (1.1.6-8)
In the Prologue of Romeo and Juliet that is spoken by the Chorus, who introduce the play to the Elizabethan audience, the term "star-crossed" would be one quite familiar to these Elizabethans. For, the stars are part of the Chain of Being. When one part of this chain is upset, as in the stars, then there is disorder and chaos. So, when the stars are taken out of their order, things go awry and fate changes the order of things.
Therefore, when Romeo and Juliet have their stars taken out of order and "crossed," they become fated lovers, lovers to whom misfortune will come. Thus, their lives contain a destiny that will prove tragic for them. In modern times, one would say that they have bad luck, such as when they meet and their families are in a feud against one another; or, when Romeo happens upon Mercutio and Tybalt fighting and he inadvertently kills Tybalt; or, when John cannot get the Friar's message to Romeo because Mantua is quarantined; or, when Friar Laurence runs out of the catacombs and Juliet is left alone to her fate.