Take a bunch of skittles and toss them onto a table. Draw a line on the table that best represents the skittles. This is linear regression with one predictor.

Now imagine you could toss those skittles and have them suspend at different heights above the table. Where would you place a sheet of paper so that you could best represent the position of all the skittles. This is linear regression with N predictors.

Now imagine you could toss the skittles into N-dimensions. What N-dimensional surface would best represent the position of all the skittles. This is linear regression with N predictors.