Servius, in his note on Aeneid 1.10, has a very straightforward, no-frills, useful definition of what it means for Aeneas to be insignem pietate:
quia patrem et deos penates de Troia sustulit.
And that pretty much sums it up. He then connects this to Vergil’s reason for invoking the Muse: he had to invoke her assistance because of the apparent contradiction involved in Aeneas’ pietas on the one hand and the anger of the gods toward him on the other:
et hic ostendit merito se invocasse musam. nam si iustus est Aeneas, cur odio deorum laborat?
Juno, obviously, is Aeneas’ main problem; but her anger leads Aeneas to suffer at the hands of the gods more broadly (vi superum, saevae memorem Iunonis ob iram, 1.4).