to plunge something fully into water, and from that picture, to wash in water as a religious act or to be wholly engulfed by something
At its root this word means to dip or sink something so that it goes completely under. Outside the Bible it is used of ships going down, of a sword driven in to the hilt, and of a person held under to drown. That physical picture of going all the way under is the source of everything else the word does.
From that core the word stretches in two directions. One direction is religious washing: when you immerse yourself or are immersed in water for cleansing or as a covenant act, you are baptized. This covers both the Jewish purification baths of Jesus' day and, above all, the new rite of John and the early church, where a person was put under the water as a sign of repentance and of belonging to Jesus.
The other direction is a vivid word-picture. Just as someone can be plunged under water, a person can be plunged under a flood of trouble, swept up into a leader's cause, or saturated by the Holy Spirit. The New Testament uses the word all three of these figurative ways, and each one works only because the literal sense of being totally surrounded and overwhelmed is doing the imaginative work underneath.
These are not separate, unrelated words. They are one idea seen from different angles, so the reader who pictures full immersion will understand each use rightly.