No matter which Arduino or compatible board you're using - some ideas or projects will require more digital inputs. You could be making your own customised keyboard, a large control panel, or sensing the output from many digital devices. The solution to problems like this is to use an I/O expander IC, and one example is the NXP PCF8575.
The use of this expander with Arduino has been explained by Instructables member FuzzyWobble who shows us the required hardware connections and the matching Arduino sketch examples to read the inputs from one or more PCF8575s using the I2C bus. Once you have an understanding of the Arduino Wire library it's quite simple, and opens up using many other parts as well. Finally a quick demonstration of the example circuit is shown in the following video: