Translation

• to have no opportunity
• no way (of doing sth)
• no chance
• no connection
• not placed (in a competition)
• (in pop lyrics) no chance of love, no place to be together etc

Examples

• 有缘千里来相会，无缘对面不相逢。
  Those fated to meet will do so regardless of distance. Those not fated will not, even if they are across from one another.