Answer

Usually the Sages interpret expressions like "an eternal statute" to say that some law applies at all times, even in a context where it might otherwise have been annulled. (With regard to sacrificial matters, they expound the word "statute" to say that it is indispensable.)
The assumption is that the entire Torah does not change and is not annulled, but there are sometimes conditions within a law such that in their absence the law should lapse for halakhic reasons. Here a word like "statute" can indicate that the law should not be annulled. Or there may have been an initial assumption that the law should be annulled for some reason, and therefore this word is needed to say that it should not be annulled.
An example: in the conversion process, the presentation of bloods—that is, a sacrifice—is required. Seemingly, that would mean that when the Temple no longer stands, it is impossible to convert. The Talmud in Keritot 9a raises this difficulty:
Hence now, when there is no sacrifice, should we not accept converts? Rav Acha bar Yaakov said: "And if a stranger sojourns with you… throughout your generations" etc.
It expounds the words "throughout your generations" to say that when it is impossible to offer the sacrifice, one may convert even without a sacrifice.