Parallel lines are lines that lie on the same plane and do not intersect at any point. In other words, they are always the same distance apart and will never meet or cross each other.

Explanation:
To understand why parallel lines do not intersect, we need to understand a few concepts related to lines and planes.

1. Definition of a line:
A line is a straight path that extends infinitely in both directions. It has no endpoints and can be represented by a straight line with two arrowheads.

2. Definition of a plane:
A plane is a flat surface that extends infinitely in all directions. It is two-dimensional and can be thought of as a tabletop or a wall.

3. Intersection of lines:
When two lines intersect, they meet or cross at a single point. This point is common to both lines.

Now, let's consider two lines in a plane. If these lines are parallel, they will never intersect. This can be visualized by imagining two train tracks. The tracks are always the same distance apart and run alongside each other without ever meeting.

Key Points:
- Parallel lines lie on the same plane.
- They are always the same distance apart.
- Parallel lines never intersect or meet at any point.
- Parallel lines can be represented by the symbol "||" (two vertical lines).

In conclusion, parallel lines are lines that lie on the same plane and do not intersect at any point. They are always equidistant from each other and can be represented by the symbol "||". Understanding parallel lines is important in various fields, such as geometry, architecture, and engineering.