Export is a way to dump the contents of your container into a .tar.gz, or a stream to put into some other place. For example, you could stream this into an in memory tar in python.

Here we export an image into a .tar file:

singularity export container.img > container.tar

And here is the recommended way to compress your image:

singularity export container.img | gzip -9 > container.img.gz