Before you understand distance of line from a point, you are advised to read
What is a Line ?
What is a Perpendicular ?
Observe the following diagram which have a line XY and a point Z.
Now, from point Z if you want to go to line XY, you can choose any of the below shown path:
Now you can notice there are several paths to reach line XY i.e. ZA, ZB, ZC, ZD, ZE and ZF
But which path you would choose to reach line XY ?
Of course, you would like to choose the shortest path.
This shortest path is ZD and ZD is also perpendicular to XY & we get:
The length of perpendicular from a point to a line is the shortest distance from the point to the line.
And the length of perpendicular is also known as distance of the line from the point.
Therefore, this gives a property "The length of perpendicular from a point to a line is the distance of line from the point"

