Eternal formats are DCI tournament formats which allow cards from all Magic: The Gathering sets with the standard card back and non-silver-bordered card frames.
The two official formats are Vintage and Legacy.[1][2]
Colloquial Use
Often formats which are not DCI tournament formats like Pauper or Commander are also described are eternal, since they allow use of all Magic editions.
An even broader definition includes all formats without rotation like Modern.