This is a really broad question, but there are two tools which can help you to create unique graphic effects in Unity:
- Programming your own shaders gives you a lot of freedom to develop graphic effects on the GPU
- The Mesh class gives you access to your 3d models. You can use it to deform or even generate new 3d objects at runtime.
And then there is of course a lot of cool stuff you can do with the special effect tools Unity provides to you out-of-the-box:
- The post processing system can add all kinds of neat visual effects to the whole camera. You can even program your own.
- Particle effects
- Line Renderers
- Trail Renderers