**Answer:**

The correct answer is option A, "plane".

A **plane** is a flat surface that extends infinitely in all directions. It is a two-dimensional surface that has length and width but no thickness. A plane can be thought of as an imaginary sheet of paper that goes on forever in all directions.

Here are some key points to understand about planes:

**1. Definition:** A plane is a flat, two-dimensional surface that extends infinitely in all directions.

**2. Characteristics of a Plane:**
- A plane has no thickness.
- It is infinitely large and extends indefinitely in all directions.
- It is a flat surface that can be represented mathematically.
- A plane has two dimensions - length and width - but no height.

**3. Representation:** A plane can be represented by drawing a flat surface on a piece of paper or by using mathematical equations to describe its properties.

**4. Examples:** Some examples of planes include:
- The surface of a table or a whiteboard.
- The floor or ceiling of a room.
- The surface of a lake or a pool.
- The surface of a piece of paper.

**5. Use in Geometry:** Planes are an important concept in geometry. They are used to define and describe geometric shapes and figures. For example, a square is a flat shape that lies in a plane, and a cube is a three-dimensional shape made up of six square faces that are all in different planes.

In conclusion, a flat surface that extends indefinitely in all directions is called a plane. It is a two-dimensional surface with length and width but no thickness. Planes are important in mathematics and geometry for defining and describing shapes and figures.