What is a linear regression?
A linear regression is a mathematical-statistical way to express the linear relation between an outcome/response variable, and one ore more explanatory variables.
For example how can a persons weight can be expressed as a function of his height?
In this example - the weight is the outcome/response variable, and the height is the explanatory variables.
If we take a random sample of 10 mens heights and weights, we would for example get something like this:

Generating and plotting the data and the regression line:

men<-data.frame("height"=c(160,180,175,201,188,173,182,166,192,178), 
                "weight"=c(60, 85, 81, 87, 77, 74, 80, 72, 91, 86))
men_lm<-lm(data=men,weight~height)
plot(x=men$height,y=men$weight,col="blue",pch=19,xlab="Height (cm)"
     ,ylab="weight (kg)",main="men linear regression \nfor weight vs height")
abline(men_lm,lwd=2,col="red")

Application for playing around with linear regression
In the bellow url - you can find an interactive application that enables you to enter 4 points on an x-y axis, and see the linear regression line that is generated upon their values.
Linear regression interactive applocation
You should choose 4 points with x and y values, each between -100 and 100.
The points will be shown on the plot, along with the linear regression line that fits them.
You can see that changing the points coordinates, changes the regression line.
You can also coose if want to show in the plot each of the following elements:
1. The 4 points
2. The regression line
3. The legend