Parallel lines are straight lines in a plane that never meet or intersect, no matter how far they are extended. They maintain a constant distance from each other, which means they have the same slope when graphed on a coordinate plane. In geometry, parallel lines are often denoted with the symbol ||. For example, if line AB is parallel to line CD, it can be written as AB || CD. This concept is fundamental in various fields, including architecture and engineering, where maintaining consistent distances is crucial for structural integrity.