Emersion is when something that's been out of sight appears or emerges. The emersion of your friend's head from the water is a relief if he's been holding his breath at the bottom of the pool for a really long time.
It's especially common to use the noun emersion when you're talking about something or someone rising from the water after being submerged beneath the surface. On a whale watch, people gaze at the ocean hoping to see the emersion of a whale, and in many harbors you can also see the emersion of seals' heads if you watch the water long enough. It's easy to confuse emersion with its opposite, immersion. Emersion shares a Latin root with emerge — emergere, "rise up."