What's the meaning of 缘分 in English?
Wikipedia has a very good explanation of the concept of 缘分:


  Yuan (simplified Chinese: 缘; traditional Chinese: 緣) or Yuanfen
  (simplified Chinese: 缘分; traditional Chinese: 緣分; pinyin: yuánfèn;
  Vietnamese: duyên phận) is a Buddhist-related Chinese concept that
  means the predetermined principle that dictates a person's
  relationships and encounters such as the affinity among friends or
  lovers. In common usage the term can be defined as the "binding force"
  that links two persons together in any relationship. The concept of
  synchronicity from the Swiss psychologist Carl Jung can be seen as
  similar to yuánfèn,[citation needed] which Chinese people also believe
  to be a universal force governing the happening of things to some
  people at some places. Yuánfèn belongs to the family of concepts known
  in theology as determinism.
  
  Some believe that the driving forces and causes behind yuánfèn are the
  actions done in the previous rebirths. Therefore, it can be understood
  as the relational- as opposed to the physical- aspect of karma in
  Buddhism. However, while karma often refers to the consequences of an
  individual's actions on him- or herself, yuán is always used in
  conjunction with two persons.


and 有缘无分:


  The proverb yǒu yuán wú fèn (有緣無份), "Have fate without destiny," is
  sometimes used to describe couples who meet, but who do not for
  whatever reason stay together.


Other than the above, I would like to add my own interpretation as follows:

In modern day practice, 缘分 is used more seriously to describe a relationship between lovers, whereas 缘 is used more casually to describe the chanced encounter between friends. For example:


  我俩的缘分已尽，还是分手吧。(This is the end of our relationship, let's split up.)
  
  我跟你真的很有缘，走到哪里都可以碰面。(The two of us are so fated together that wherever
  we go, we tend to meet up.)


The character "分" is originally written as "份" and is still very much in use today. "份" has the meaning of a share or a portion, e.g. "股份", "名份", "福份". Therefore, 有缘无分 (expanded as 有缘相爱，无份相守) can be taken to mean two persons having the fate (inevitable turn of events) to meet and become lovers, but not having the destiny (destination, the end result) to share the rest of their lives together as husband and wife.