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The definition of parallel lines are lines that do not intersect and lie in the same plane.
When applying this concept of parallel lines to euclidean geometry, we could say that since there are multiple postulates and theorems (as you will see later) that help us with defining parallel lines, we can identify them in reality. For instance, if we know the properties of parallel lines, then we can show that train tracks (for example) are parallel to each other.
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Euclidean geometry goes hand in hand with the parallel postulate, which states that if there is a point that is parallel to a line, then there is exactly one line through it.
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