What does it mean by 'All beings have a Buddha nature'? I have come across this phrase while studying Zen, in a Zen meditation center. It is Dogen's translation of Nirvan Sutra. That all beings by nature are Buddha. As I understand, we become Buddha when be are enlightened. We have to strive through Right Effort to become Buddha, isn't it? 

What does this phrase mean to you?
It is not just Dogen's translation. The Nirvana Sutra states that all beings have Buddha Nature. You can also check Mark Blum or Yamamoto's translations.

However, Dogen played with the initial statement. He rephrased "All beings have Buddha Nature" in "All beings are Buddha Nature." I will not explain this point because you did not ask.

The meaning of "All sentient beings have Buddha Nature" is that all sentient beings have the potential to achieve full enlightenment. However, the entity of Buddha Nature is debatable. The following interpretations are traditional:


Buddha Nature as the suchness of the mind of a sentient being. From this viewpoint, a buddha does not possess Buddha Nature because he is not sentient.
Buddha Nature as the resultant dharmakaya. A buddha possesses it, a sentient being does not. You can think of "Buddha Nature" in this context as "What characterizes a Buddha".
Buddha Nature as the mind-basis-of-all (Alaya-Vijnana)
Buddha Nature as a seed in the mind-basis-of-all. From this viewpoint, we would have to water the seed for it to sprout.


When the Clouds Part: The Uttaratantra and Its Meditative Tradition as a Bridge between Sutra and Tantra explains traditional presentations of Buddha Nature. It is a must read.

I cannot remember the passage, but Dogen despised the idea that "We are already buddhas but just don't know it". This idea is that of the original enlightenment doctrine. More importantly, In chapter Ten (On the Four Truths),   the Nirvana Sutra itself states:


  A person might say: "I have already attained unsurpassed
  Enlightenment! Why? Because I have the Buddha-Nature. Any person
  possessing the Buddha-Nature has assuredly attained unsurpassed
  Enlightenment. Consequently, I attain Enlightenment." Then, one should
  know, such a person infringes the parajika. Why so? There surely is
  the Buddha-Nature. But not yet having practised the best expedient of
  the Way, the person has not yet seen it. Having not yet seen it, there
  can be no attaining of unsurpassed Enlightenment. O good man! On this
  account, the teaching of the Buddha is profound in its meaning and
  difficult to fathom.