Most digital pianos offer a variety of different sounds, but it is the acoustic piano sounds that are the most important as they are the sounds that will be used the most. A digital piano will usually offer an acoustic piano sound suitable for classical music, jazz and even for pop.
To emulate the complex sound of an acoustic piano, a digital piano uses a technology called sampling. Expensive microphones are used to record or 'sample' the sound made when a key is depressed on an acoustic piano. These samples are then stored in memory and played back each time you play the keys.
The better the sampling technology, the better the digital piano sound will be. Let's start with how many notes should be sampled. An acoustic piano has 88 notes, each of which has a different character due to the different length of strings and the type of metal used. While a quality digital piano will use 88 individual samples, a budget digital piano will often use a sample every third or fourth note and synthesise the notes in between. This keeps costs down but makes for a less convincing piano sound.
An acoustic piano has an extremely wide dynamic range from very soft to very loud. But it is not just the volume that changes the harder you strike a key. The tone also changes. To recreate this change in tonal character, many digital pianos will use several samples per note - the idea being that if you play softly, you will trigger a sample taken from an acoustic piano that was played softly and if you play hard, you will trigger a sample that was taken from an acoustic piano that was played loudly. Some digital pianos go even further. Using a technology called Supernatural, they can emulate the very smooth and natural way an acoustic piano responds to a player with no audible steps in the sound.
One interesting characteristic of a piano note is that it can sustain for several seconds, but after the first couple of seconds, much of the initial complexity of the sound has gone. The remaining seconds of sound don't change that much as they gradually decrease in volume. Rather than devote memory space to sampling the whole note, some digital pianos repeat or loop a section of the decaying sound at gradually reduced volume levels.
Just as an acoustic piano can be voiced to suit the player's tastes or the room that it is in, so too can today's digital pianos. Rather than live with one or two piano sounds that may or may not inspire, some digital pianos let you adjust all kinds of parameters to create your own personal piano sound or to adjust the sound to the acoustic properties of the room that you are playing in. Some even let you do this via an iPad.
And should you get bored of an acoustic piano sound, virtually all digital pianos offer additional sounds such as harpsichords, electric pianos or strings that might better suit the style of music that you are playing.