The following quote comes from a recent work on early Christian history; on the topic of early Christian worship, we have this gem on their understanding of "remembrance" (Greek: αναμνηεσις) which ties into a previous post I did on the issue:
Ivor J. Davidson, The Birth of the Church: From Jesus to Constantine, AD 30-312 (Grand Rapids, Mich.: Baker Books, 2004), 281.
In Justin’s account, the prayer said at the Eucharist is extemporaneous, and this is likely to have been the general rule. From other second- and third-century witnesses, we can possibility glimpse something of the broad pattern such improvised prayers may have taken. In accordance with Jewish traditions of giving thanks at meals, Eucharistic prayers seem often to have consisted of at least two aspects: remembrance (Greek, anamnesis) and invocation (Greek, epiclesis). Remembrance meant recollecting the saving acts of God in the history of Jesus and perhaps reciting the words of Jesus at the Last Supper as an institutional narrative for the meal. Invocation meant appealing for the Holy Spirit to come upon the worshipers and to accept their thanksgiving.
Ivor J. Davidson, The Birth of the Church: From Jesus to Constantine, AD 30-312