Nerves can be your best friend or your worst enemy as a pianist. Performing takes a lot of energy which can be derived from "nerves." As adrenaline surges through your system, you can learn to harness that energy for an electric performance.
Unharnessed, that energy manifests itself in a variety of ways that frustrate and discourage students. Sweaty palms, shaking hands, a fast heartbeat etc. These things can interrupt a performance and cause a musician to make mistakes in places they never have before. This can take the joy out of performing.
The secret is learning to gather that nervous energy and use it to enhance your performance. There are many ways to do this. One method that I like to use is a mental conditioning that prepares a student to see their music as a gift they are giving to their audience. If this is your perspective, the pressure is taken off of you as the performer because you are offering your audience something special and it's hard to be nervous when you are giving.
I encourage my students to mentally place themselves in a safe place while they are performing. I tell them to imagine they are inside a glass box where no one can hear them play. After a piece is over, the applause begins and I invite them to rejoin the audience. This is a trick that has worked well for me. I often picture a barrier between myself and my audience, some space with which to work, I can breathe, thus recreating the solitude which is so familiar to me during practice.
Another secret is simply listening deeply to your music. Connect to it. If you are wrapped up in the beauty of the music you are playing, you will be less likely to slide into a nervous heap. The key is to hear the music in your head, to sing along with it internally. The rest will happen naturally.
I also invite my students to lean into my strength as a teacher. At a recent recital I took a nervous student aside before the performance and asked her to hold my hands as she transferred all her nervous energy into me. I became the container that held her nerves so she could be free to perform. With her nervous energy out of the way she was able to create a breathtaking performance with solid musicality and thus created positive memories that will last a lifetime.