Imagine a line going through a pack of points. That line is going to be called a best-fit line, or a trend line, or a regression line. The idea of a line of best fit is that it will roughly approximate what's going on with the data in the form of a single line.
EXAMPLE
Suppose we have the following scatterplot.
Roughly half the points fall above and below the line. In this particular example, about five of them are fairly near the line, three are substantially below, and three are substantially above.
A good best-fit line will have the following features:
EXAMPLE
This is a poor choice of a trend line. It does not cut the "oval" the long way, and there is a pattern to how the points are above or below the line. With this trend line, any point below the line is off to the right, and any point above the line is off to the left.
EXAMPLE
Below is a better trend line, because the points that are above and below are peppered throughout. You don't want a pattern to how the points are off from the line.
What is a trend line used for? A line of best fit is used to give approximations for values of x and values of y--even on places where there is an existing value of y.
EXAMPLE
In the scatterplot below, when x equals 6, there's a difference between the actual value of y at 6, and what the line predicts as the value of y at 6.
Source: Adapted from Sophia tutorial by Jonathan Osters.