While Easter sure comes with a significant religious meaning, it seems to be distinctly its more earthly and mundane aspects that are emphasised in Faust. Though, the connections to resurrection aren't there for nothing either and surely intertwined with its less religious importance.
If we take a look at the situation when we're introduced to Easter, through the Easter bells ringing right when Faust is about to end his life, we see that Faust himself doesn't care too much about the religious aspects either, they only remind him of the experiences that are beyond his reach:
|Die Botschaft hör' ich wohl, allein mir fehlt der Glaube
Das Wunder ist des Glaubens liebstes Kind.
Zu jenen Sphären wag' ich nicht zu streben,
Woher die holde Nachricht tönt;
|I hear your message, but faith fails me:
The marvelous is faith’s dearest child.
I don’t attempt to rise to that sphere,
From which the message rings:
Rather than that, it makes him recall the memories of his youth, where he was still striving full of energy and free from the hopeless realization of scholarly impotence that he's facing now:
|Da klang so ahndungsvoll des Glockentones Fülle,
Und ein Gebet war brünstiger Genuß;
Ein unbegreiflich holdes Sehnen
Trieb mich durch Wald und Wiesen hinzugehn,
Und unter tausend heißen Thränen,
Fühlt' ich mir eine Welt entstehn.
Dieß Lied verkündete der Jugend muntre Spiele,
Der Frühlingsfeier freies Glück;
Erinnrung hält mich nun, mit kindlichem Gefühle,
Vom letzten, ernsten Schritt zurück.
|The bell notes filled with presentiments,
And a prayer was pleasure's call:
A sweet yearning, beyond my understanding,
Set me wandering through woods and fields,
And while a thousand tears were burning
I felt a world around me come to be.
Love called out the lively games of youth,
The joy of spring's idle holiday:
Memory's childish feelings, in truth,
Hold me back from the last sombre way.
This relates back to his earlier mournings of reaching a dead end in his studies and in what we are able to learn and know. We see this also in his earlier conversation with his student Wagner, a "bookworm" par excellence, where he looks down cynically onto Wanger's optimism towards gaining knowledge from reading the thoughts of past researchers who came to the same hopeless realization that Faust is facing.
He basically has lost his will to strive and experience (and ultimately to live) for there is nothing to gain anymore, and the Easter bells are calling back that youthfull naiveté and optimism to some degree. And you'll notice how he says that it's "spring's idle holiday". It is the mundane qualities of Easter as a social holiday and the beginning of spring that calls him back to life, not the sublime religiosity that only proclaims spheres he can't and won't reach anyway.
This is strengthened by the following scene at the city gates, where we first see all kinds of merry folk going about their holiday business, as well as in the "Osterspaziergang", one of Faust's most famous monologues while he walks the streets with Wagner. It sets off by classic natural descriptions of spring's awakening and winter's retreat, while then juxtaposing that with the social awakening of civilization from winter's drabness:
|Vom Eise befreit sind Strom und Bäche,
Durch des Frühlings holden, belebenden Blick,
Im Thale grünet Hoffnungs-Glück;
Der alte Winter, in seiner Schwäche,
Zog sich in rauhe Berge zurück.
Überall regt sich Bildung und Streben,
Alles will sie mit Farben beleben;
Doch an Blumen fehlts im Revier,
Sie nimmt geputzte Menschen dafür.
Kehre dich um, von diesen Höhen
Nach der Stadt zurück zu sehen.
Aus dem hohlen finstren Thor
Dringt ein buntes Gewimmel hervor.
Jeder sonnt sich heute so gern.
Sie feyern die Auferstehung des Herrn,
Denn sie sind selber auferstanden,
Ich höre schon des Dorfs Getümmel,
Hier ist des Volkes wahrer Himmel,
Zufrieden jauchzet groß und klein:
Hier bin ich Mensch, hier darf ich’s sein.
|Rivers and streams are freed from ice
By Spring's sweet enlivening glance.
Valleys, green with Hope's happiness, dance:
Old Winter, in his weakness, sighs,
Withdrawing to the harsh mountains.
Change and growth are everywhere,
He enlivens all with his colours there,
And lacking flowers of the fields outspread,
He takes these gaudy people instead.
Turn round, and from this mountain height,
Look down, where the town's in sight.
That cavernous, dark gate,
The colourful crowd penetrate,
All will take the sun today,
The Risen Lord they'll celebrate,
And feel they are resurrected,
I hear the noise from the village risen,
Here is the people's true Heaven,
High and low shout happily:
Here I am Man: here, dare to be!
The same how spring reinvigorates nature as well as humanity, the same it reinvigorates some of Faust's life spirits, be it only the more mundane spirits realizing that there is more in life than just knowledge. This can be seen as well in relation to his ealier struggles that contrast the gaining of knowledge and ascension into higher spheres with his clinging to the enjoyment and experience of earthly life:
|Du bist dir nur des einen Triebs bewußt,
O lerne nie den andern kennen!
Zwei Seelen wohnen, ach! in meiner Brust,
Die eine will sich von der andern trennen;
Die eine hält, in derber Liebeslust,
Sich an die Welt, mit klammernden Organen;
Die andre hebt gewaltsam sich vom Dust,
Zu den Gefilden hoher Ahnen.
|You only feel the one yearning at best,
Oh, never seek to know the other!
Two souls, alas, exist in my breast,
One separated from another:
One, with its crude love of life, just
Clings to the world, tenaciously, grips tight,
The other soars powerfully above the dust,
Into the far ancestral height.
So to sum up, to me Easter here, by marking the return of spring as well as in its significance as a joyful holiday, serves as both a reinvigoration of Faust's spirits and his nature to strive as well as a reminder of the mundane qualities of life and the merits of experience and enjoyment contrasted to studying and book-based knowledge which Faust feels to have wasted his life on. And this in turn might just bring him into the proper mindset for a fruitful temptation by Mephisto.
I won't claim the above explanations to be the end of the story, though. I'm far from an expert on the topic and all that is based on a reread inspired by the question. I'm sure this has been studied time and time again and there might be more to Easter's significance under the hood. And even when seeing this angle of spring and revitalization, the connection to Christian resurrection isn't too hard to draw, in fact the very words of the work already do that (neither would the celebration of Jesus's resurrection at the very beginning of nature's be entirely coincidental in the first place).
The English translation presented here was taken from the website Poetry in Translation.