The character 天 tiān literally means "sky" but can also be used to refer nature. I this latter sense, it can refer both to the natural world in general and to the specific natures of individual things (which I take it to be their participation in the general nature). There is also another term, 性 xìng, which refers only to specific natures and became a focus of Guo Xiang's influential interpretation of Zhuangzi but is notably absent from the Inner Chapters.
Depending on context, I translate it as "heaven," "nature," or sometimes "sky." What is its significance? The changes in the sky--the rising and setting of the sun and moon, the movements of the constellations (one meaning of the term 天道tiān dào, "the way of heaven"), and the alternation of the seasons--are the motive force behind all life. Also, as Mozi put it, 何以知天之愛天下之百姓？以其兼而明之 (Mozi 7.1.5), "How do we know heaven loves all the people in the world? Because it shines on them all equally." The sky covers everyone. Nature has room for all things. Mohist argumentation starts from a definition of terms. But the problem with definition of terms is that it rules out all the other possible definitions, other perspectives and ways of framing the question, which was exactly what Zhuangzi was trying not to do.