An analogue piano is the precursor to the electric piano. These are pianos that use knobs to be able to work with the piano. Despite having knobs the music from an analogue piano is still produced by instrumental methods. That means you still get a very rich sound and still have the feeling of a traditional piano with some added benefits. They are somewhat similar to an electric guitar.
What really makes an analogue piano so nice is that they are often times lightweight and easy to move around. They are very similar to an electric piano. That being said, you can get analogue pianos in a wide variety of designs. You can get one that really matches what you are looking for. There are even grand pianos with the features of an analogue piano.
Another name for this kind of piano is a stage piano. Examples of an analogue piano include the Fender Rhodes, Wurlitzer, and more modern digitalized analogue pianos. These pianos are often picked by those who wish to have a classic sound with a more modern design.