The main playing difference between a digital piano and a real piano is the key action. Depending on how much you want to spend you can get realistic key feel and action on a digital piano.

Merriam Music (a Canadian music shop) recently made a couple of interesting videos talking about Kawai's different key actions on their various models of digital piano:

https://www.youtube.com/watch?v=8oRWQ6OVqq0

https://www.youtube.com/watch?v=V6f6-sx4b-c

The Kawai ES110 (soon to be replaced by the ES120), for example, is a solid entry level digital piano at a good price. As you progress with playing you might find you want more out of the key action than the Responsive Hammer Compact action on the ES110 offers, in which case getting a model with the Responsive Hammer III action is a good upgrade.

I like digital pianos because they can be cheaper than the real thing, they don't require tuning, they are smaller, lighter, more portable with audio out, MIDI, and bluetooth connections for integration with software. I like that I can play it silently (or at least quietly) with headphones whenever I want.