In architecture, an apse is a curved or rounded section at one end of a building. You'll most often find an apse in a church.
In Gothic, Romanesque, and Byzantine Christian churches, it's very common to find a semicircular area with a vaulted ceiling, often topped by a dome, on the east side of the building. This is generally where the altar is located, making the apse the most important section of the building. The word comes from the Latin apsis, "arch or vault," and the Greek root hapsis, "arch or loop."