The region between an arc and the two radii joining the center of the endpoints of the arc is called a sector. Let's break down the answer and explain it in detail.

The Meaning of the Terms:
- Arc: In geometry, an arc is a part of the circumference of a circle.
- Radii: Radii (plural of radius) are the line segments that connect the center of a circle to any point on its circumference.
- Center: The center of a circle is the point equidistant from all points on the circumference.

Understanding a Sector:
A sector is a region enclosed by two radii and an arc. It resembles a "slice" of a circle, similar to a slice of pizza or a piece of pie. The radii form the two straight sides of the sector, and the arc forms the curved side.

Properties of a Sector:
- The center of the circle lies at the vertex of the sector.
- The angle formed by the radii at the center of the circle determines the size of the sector.
- The length of the arc that forms the curved side of the sector is proportional to the angle it subtends at the center of the circle.

Applications of Sectors:
Sectors have various applications in real life, including:
- Calculating the area of a sector: The area of a sector can be found using the formula A = (θ/360) * π * r², where θ is the angle of the sector in degrees and r is the radius of the circle.
- Solving problems involving angles and measurements: Sectors are used in trigonometry and geometry to solve problems related to angles, lengths, and areas.

Conclusion:
In conclusion, the region between an arc and the two radii joining the center of the endpoints of the arc is called a sector. Sectors are important geometric shapes that have various applications in mathematics and real-life scenarios.