Here is the way I understand this statement of God being Love:
Religion must be founded upon and built up in Love, for God is Love, and love in the Bible is never a ‘feeling’ but is always something which is active - hence why the word used most in the New Testament for love is “agape” or “charity” - a ‘self-giving’ love. The second word used for love in biblical greek is ‘phileo’ or brotherly love. Religion cannot be lived by oneself or for oneself. Religion connects us with the human race at large and gives us a universal vision of reality. The word religion comes from the Latin religio which means “to bind” or “to connect”. Religion therefore connects us with the human race at large and gives us a universal vision of reality. The very essence of this rests upon Love.
And so in Catholicism Love is held to be all-embracing, never confined, never differentiated, never partial as the great Dominican mystic and Pope Leo XIII explained:
“…This beard has many hairs, but they all make up one beard, so that they all receive the benignant oil that flows into it. That hair, however, that would separate itself from the whole, be it ever so small, would receive not a single drop of the precious charism. The same is true of love. As long as it is all-encompassing, as long as it shares its graces without making distinctions, it will remain the precious and mellifluous chrism of all good; but as soon as you exclude anyone or anything from your love, you receive nothing of this oil. Beloved, take very good care that your love embraces everyone. Show charity toward all and deprive no one of his peace!..”
- Johannes Tauler (c.1300-1361), Catholic mystic and Dominican
“…The maternal love of the Catholic Church embraces all people…It is the industrious guardian of the teachings of its Founder [Jesus] who, by His words and those of the apostles, taught men the fraternal necessity which unites the whole world. From Him we recall that everybody has sprung from the same source, was redeemed by the same ransom, and is called to the same eternal happiness…”
- Pope Leo XIII, CATHOLICAE ECCLESIAE, 1890
This all stems from the Catholic/Christian of God as “Love”.
The Christian conception of the Oneness of God is that of a Tri-unity of Persons united by one, common essence and by their mutual self-offering and self-giving of each other, and in Catholic Christianity united by the bond of Love between the Father and the Son that is the Holy Spirit. In this utter abandonment of self-will, the three Persons are One God, one Being, sharing one Unknowable Divine Essence. Pope John Paul II stated in his apostolic letter *Mulieris Dignitatem * that “Man – whether man or woman – is the only being among the creatures of the visible world that God the Creator has willed for its own sake; that creature is thus a person. Being a person means striving towards self-realization, which can only be achieved through a sincere gift of self. The model for this interpretation of the person is God himself as Trinity, as a communion of Persons.”
True love is the relationship between the three persons, who each selflessly empty themselves for one another. Each of the persons of the Trinity lives completely for the others; each is a complete gift of self to the others. This complete self-giving not only constitutes the individual persons of the Trinity, but also their inseparable oneness. Thus, for Christians the very basis of all reality is the loving communion of persons that is the Holy Trinity.
Pope Benedict XVI once said:
“…The beginning of Christian existence is not an ethical decision or a sublime idea, but rather the encounter with an event, with a person, who gives life a new goal and at the same time, a sure growth…Today we contemplate the Most Holy Trinity as Jesus introduced us to it. He revealed to us that God is love “not in the oneness of a single Person, but in the Trinity of one substance” (Preface). He is the Creator and merciful Father; he is the Only-Begotten Son, eternal Wisdom incarnate, who died and rose for us; he is the Holy Spirit who moves all things, cosmos and history, toward their final, full recapitulation. Three Persons who are one God because the Father is love, the Son is love, the Spirit is love. God is wholly and only love, the purest, infinite and eternal love. He does not live in splendid solitude but rather is an inexhaustible source of life that is ceaselessly given and communicated. To a certain extent we can perceive this by observing both the macro-universe: our earth, the planets, the stars, the galaxies; and the micro-universe: cells, atoms, elementary particles. The “name” of the Blessed Trinity is, in a certain sense, imprinted upon all things because all that exists, down to the last particle, is in relation; in this way we catch a glimpse of God as relationship and ultimately, Creator Love. All things derive from love, aspire to love and move impelled by love, though naturally with varying degrees of awareness and freedom…The strongest proof that we are made in the image of the Trinity is this: love alone makes us happy because we live in a relationship, and we live to love and to be loved. Borrowing an analogy from biology, we could say that imprinted upon his “genome”, the human being bears a profound mark of the Trinity, of God as Love…”
Our God is not just an individual remote from this universe, who needs intermediary beings to come between Himself and his children. As transcendent and exalted beyond all our imaginings as He is, beyond all thought or human conceptions He emptied Himself and came down as one of us to offer relationship to us.
Nor is He simply an individual - a single person. God, as we Christians know Him, is social in His very being, because He is not just one person but three- God is a perfect social unity, a perfectly intimate divine community, a family. And he invites us to share, as much as we can, in this divine inner life, to be embraced in this unity and live in unity and harmony with God and with one another with He in Us and We in Him. That perfect divine life is our model, and the life into which we are invited.
As Pope John Paul II once explained:
“…In the depths of our being, where not even our gaze can penetrate, the Father, Son and Holy Spirit, one God in three persons, are present through grace. Far from being a dry intellectual truth, the mystery of the Trinity is the life that dwells in us and sustains us…The mystery of the origins from which all things flow, God appears to us as the One who is the fullness of being and communicates being, as the light that “enlightens every man” (cf. Jn 1: 9), as the Living One and giver of life. He appears to us above all as Love, according to the beautiful definition in the First Letter of John (cf. 1 Jn 4: 8). He is love in his inner life, where the Trinitarian dynamism is the very expression of the eternal love with which the Father begets the Son and both give themselves to each other in the Holy Spirit. He is love in his relationship to the world, since the free decision to make it out of nothing is the fruit of this infinite love which radiates into the sphere of creation. If the eyes of our heart, enlightened by revelation, become pure and penetrating enough, they can by faith encounter this mystery in which everything that exists has its root and foundation…”
Hope this helps