How can multiple buffering make program faster

Question

I have some question on multiple buffering in OpenGL. For example, I have a program. It does following things:

1. do a depth pre-pass, and write some information on the shader storage buffer.
2. use the data on the shader storage buffer draw something on the default framebuffer and swap the buffer, so I can see the picture

Since I only create one shader storage buffer. GPU can't do the next framebuffer's step 1 'do a depth pre-pass', until the last framebuffer finished step 2 'use the data on the shader storage buffer'.

Is it true? How can I use shader storage buffer effective, when GPU is using multi buffering(suppose I have enought memory on GPU).