Membrane keypads are made of a thin, flexible membrane material. They do come in may sizes 4×3, 4×4, 4×1 etc. Regardless of their size, they all work in the same way.
One of the great thing about them is that they come with an adhesive backing so you can attach it to nearly anything. You just have to peel the paper backing off.
4×4 keypad  has total 16 keys.Beneath each key is a special membrane switch.
All these membrane switches are connected to each other with conductive trace underneath the pad forming a matrix of 4×4 grid.
If you had used 16 individual push buttons, you would have required 17 input pins (one for each key and a ground pin) in order to make them work. However, with matrix arrangement, you only need 8 microcontroller pins (4-columns and 4-rows) to scan through the pad.
The working principle is very simple. Pressing a button shorts one of the row lines to one of the column lines, allowing current to flow between them