Parallel lines are one of the most basic ideas in geometry. Most people learn about parallel lines early in their education, even in subjects other than math such as art. Despite being a very simple concept, most parallel lines we see in nature are manmade.
Identification

Parallel lines are two separate lines that always stay the same distance apart, never intersect each other, and are on the same plane.
Features

In a coordinate plane, parallel lines are determined by their slope. Lines with equal slope are parallel. Lines with undefined slope are also parallel.
Significance

Parallel lines are found everywhere in life and are used in several professions. Artists use parallel lines to create geometric patterns. The yellow lines on a road are parallel.
Misconceptions

Two lines can fail to intersect but not be parallel. These lines are called skew lines. Skew lines lie in different planes and thus do not satisfy the definition for parallel lines. For example, in a room, a line running from north to south (of the same wall) at floor level and another line extending from east to west at ceiling level would be skew.
Considerations

Parallel lines are not very common in nature. Tree trunks and sunlight are some of the few examples of natural parallel lines.
References
 Photo Credit Image by Flickr.com, courtesy of Kevin Dooley