There are many things, since there is more than one difference between a piano and keyboard.
A piano has a whippen which is the core of the piano action. Almost all the technology of a piano action is located here. It gives a modern piano the piano feel. The friction of the jack against the knuckle of the hammer shank can be felt as the key is depressed. This friction allows the pianist feel how much pressure is needed to play incredibly softly.
A piano action has an escape mechanism. To overcome this resistance, slightly more pressure must be applied once the key has reached close to the keybed. This mechanism is one component that allows for fast, repeated notes.
A piano has hammers which can be manipulated with the keys. The inertia caused by the jack applying force upward causes the hammer to strike the strings. In fact, a hammer can be put in limbo, neither striking the string nor sitting at rest. This cannot be done on a keyboard.
Once the hammer strikes the strings, the hammer is stopped in place by the backcheck assuming the key is still depressed. This can be felt through the key. The backcheck is also an important part of rapid repeated notes.
A piano action has dampers. Each damper is activated by depressing the keys to a certain point right when the key end touches the damper weight. Once contact is made, the key lifts the damper off the string allowing the string to vibrate. Each damper is slightly different in weight, the bass strings are the heaviest and progressively become lighter into the treble strings. Thus, once the key lifts the damaper, the key requires more force to depress. Also, each damper can mute a string slowly or quickly and this ability allows for legato and staccato playing.
A piano has a solid keybed with felt key stops to absorb shock. Keyboards have a different construction and it is more comfortable to play forcefully because of the shock absorption and extra resistance from components such as the escapement.
A piano has wires that vibrate and each vibration affects other wires. This gives a piano real sound and real physics. Vibrations can be collected to create massive sounds where all strings are allowed to vibrate. These accoustic properties are entirely lacking in a keyboard where sounds are reproduced electronically using binary data. Sounding one note on a keyboard will have no effect on the sound of another. This has severe consequences for pedalling because things do not blur on a keyboard that may on a piano.
As some of the examples above show, most of the differences between a piano and keyboard involve touch. A pianist will have a marked advantage to a keyboardist in virtually all areas because of the technical nuances that can be learned on a piano. These nuances are impossible on a keyboard.
Also, since making music is of utmost priority, the sound that is created by a piano is directly nuanced by the pianist. A keyboard instrument uses pre-recorded sound and only sounds that were recorded can be played back. Compare this to the virtually infinite tonal possibilities of a piano. Since sound gives the musician immediate feedback, technique is adopted to create the best tone. This cannot be done on a keyboard because only pre-recorded sounds are created.
There is only one advantage a keyboard has over the piano in terms of music-making:
When someone else sound like sh*t,
you can turn it off.
And when you sound like sh*t...
