In Genesis 21:30, witness signifies certification that the holiness of innocence is from the Divine. (Arcana Coelestia 2720)

In court, a witness is someone who saw a crime being committed, or observed something that could help determine the guilt or innocence of the person being tried. The spiritual meaning is similar; to "witness" something or to be a "witness" means to use the truth - things we know to be true - to confirm the goodness and purity of someone's motives (especially our own motives). Swedenborg teaches us that good loves, by their very nature, express themselves through true ideas. In fact, "truth" can be defined as "the expression of love." So if we want to know the quality of a love, we can assess it by looking at the quality of the ideas it produces. Are they caring toward the neighbor? Will they help make the world a better place? Are they aligned with what we know of the Lord's wishes? If the answers are "yes," then those truths bear witness to the love that inspired them. This is in part why the Ten Commandments talk about "bearing false witness" instead of simply "lying." Lying can be a relatively low-level thing, but bearing false witness involves portraying evil loves as good ones, a thing much deeper. In some places, especially Revelation and the Gospel of John, "witness" is applied to the Lord, both as a witness himself and in terms of others being a witness to him. In these cases the reference is to the greatest love, the source of all love and life: the Lord's perfect and infinite love for all humanity. And to be a witness means acknowledging that love in the form of divine truth, and the perfect humanity it describes.