Over 100 years ago, a scientist named Overton found that the ability of substances to enter into cells depended on their ability to dissolve in oils. We call these substances that dissolve in oils lipids. Overton suggested the barrier between the outside and the inside of a cell was itself a lipid or at least had a lot of lipid in it.

How do we know membranes exist if you can't see them? 
At the time when the basic ideas about membranes were being worked out, membranes could not be seen. Scientists made a reasonable guess that something like membranes must exist. Two observations led scientists to conclude membranes must exist:

1) Something was regulating how water and chemical substances were getting into and out of cells.
2) If you punctured a cell surface, stuff leaked out.