Well, first of all, it isn't a sentence without whatever came before '...which is why,' but, knowing your previous posts, I think you already knew that.
[T]he greatest reason to celebrate this 40th anniversary isn't scientific or environmental or political; it is personal....
The writer is saying that the greatest (most important) reason to celebrate the 40th anniversary (of something previously stated) is a personal one. Apparently, the event being celebrated has scientific, environmental and political significance, but, in the opinion of the writer, these are not as important as the personal significance. The sentence does not explain what this personal significance is, and we assume that the rest of the paragraph will do so.
I hope this is helpful,