An object is said to culminate when it reaches its highest point in the sky.
Seeing conditions improve significantly with distance from the horizon, and so culmination marks the optimal time to observe an object, assuming that other considerations such as twilight don't intervene.
When an object culminates, it crosses the line across the sky which connects the north and south cardinal points on the observer's horizon, passing through the zenith. This line is termed the observer's meridian.
For this reason, an object at the moment of its culmination may equivalently be described as transiting the meridian, or often simply transiting.