The verse that I thought of first is this one: John 15:4-5  Abide in me, and I in you. As the branch cannot bear fruit by itself, unless it abides in the vine, neither can you, unless you abide in me.   The dictionary uses quite a few words to define the meaning of abide.  They include: to conform to, to accept without objection, to be guided by, and to remain stable.  The word abide has a very strong connection with the word abode, meaning a place of residence.  To abide in Jesus is to make your home with him.

In our prayer of Consecration during the Eucharist, we proclaim that this Holy Sacrament has four primary benefits for the partaking believer…
who shall be partakers of this Holy Communion,
may worthily receive the most precious Body and Blood of thy Son Jesus Christ,
be filled with thy grace and heavenly benediction
and made one body with him,
that he may dwell in us, and we in him.

Let me translate all of that for you:
We who receive the bread and wine of communion
partake, not just of bread and wine, but of the precious body and blood of Jesus, as He promised.  (We call this the Real Presence)
We also are filled with the love and grace of God and His holy blessing
We are also joined together in Spirit and Body with Jesus to the extent that our existence transcends both time and space
and in that transcendent union Jesus and each of us and all of us together come to share a home together outside of this world and in the realm of what we have come to call heaven.  Or as I like to call it; our True Native Land with thee.

In the Communion Service, we literally commune with God.  We have fellowship with God even though this human body is a very poor vessel to contain such a marvel.

What it means to abide with Jesus is to make our home with Him: to welcome Him into our hearts and to open our hearts to encompass all of Heaven and Earth.