The Second Sunday of Easter brings to an end the Easter Octave; an eight-day period of particular celebration of the Resurrection.
The first eight days of the Easter season make up the octave of Easter and are celebrated as solemnities of the Lord.
One difference in the liturgy of the Easter Octave is in the dismissal at the end of Mass, which includes a double alleluia:
Go forth, the Mass is ended, alleluia, alleluia.
Thanks be to God, alleluia, alleluia.
The dismissal with double alleluia also concludes the Mass on Pentecost Sunday.