The "size" and "virtual size" describe the amount of disk space used by a container. Let me try and explain:

When starting a container, the image that the container is started from is mounted read-only. On top of that, a writable layer is mounted, in which any changes made to the container are written.

The read-only layers of an image can be shared between any container that is started from the same image, whereas the "writable" layer is unique per container (because: you don't want changes made in container "a" to appear in container "b" 😄)

Back to the docker ps -s output;

- The "size" information shows the amount of data (on disk) that is used for the writable layer of each container
- The "virtual size" is the amount of disk-space used for the read-only image data used by the container.

The reason it's named "virtual size", is that (as described earlier), the disk space for the read-only layer(s) can be shared between containers, so only take up disk space once (perhaps a different name ("shared" size?) would have been better in hindsight, but naming is hard 😄).

In the example below, I started 10 nginx containers;

CONTAINER ID        IMAGE                      COMMAND                  CREATED              STATUS              PORTS               NAMES                                         SIZE
6ca0cef8db8d        nginx                      "nginx -g 'daemon ..."   55 seconds ago       Up 54 seconds       80/tcp, 443/tcp     pedantic_mahavira                             2B (virtual 183MB)
0b75532c34d2        nginx                      "nginx -g 'daemon ..."   56 seconds ago       Up 55 seconds       80/tcp, 443/tcp     hardcore_haibt                                2B (virtual 183MB)
a86d8818795d        nginx                      "nginx -g 'daemon ..."   56 seconds ago       Up 55 seconds       80/tcp, 443/tcp     happy_pasteur                                 2B (virtual 183MB)
3e9151f0332d        nginx                      "nginx -g 'daemon ..."   57 seconds ago       Up 56 seconds       80/tcp, 443/tcp     pensive_khorana                               2B (virtual 183MB)
429c418114a1        nginx                      "nginx -g 'daemon ..."   57 seconds ago       Up 56 seconds       80/tcp, 443/tcp     nostalgic_bose                                2B (virtual 183MB)
01f6a0818b32        nginx                      "nginx -g 'daemon ..."   58 seconds ago       Up 57 seconds       80/tcp, 443/tcp     zen_davinci                                   2B (virtual 183MB)
9ed93ee43912        nginx                      "nginx -g 'daemon ..."   58 seconds ago       Up 58 seconds       80/tcp, 443/tcp     unruffled_ptolemy                             2B (virtual 183MB)
c7c17bf50744        nginx                      "nginx -g 'daemon ..."   59 seconds ago       Up 58 seconds       80/tcp, 443/tcp     zen_khorana                                   2B (virtual 183MB)
a7b0502d95ce        nginx                      "nginx -g 'daemon ..."   About a minute ago   Up About a minute   80/tcp, 443/tcp     gallant_leavitt                               2B (virtual 183MB)
8b9e9ee6c4e8        nginx                      "nginx -g 'daemon ..."   About a minute ago   Up About a minute   80/tcp, 443/tcp     clever_pasteur                                2B (virtual 183MB)
All these containers use the same image, so the "Virtual size" (183MB in the example) is used only once, irregardless of how many containers are started from the same image - I can start 1 container or a thousand; no extra disk space is used. The "Size" (2B in the example) is unique per container though, so the total space used on disk is:

183MB + 10 * 2B

Be aware that the size shown does not include all disk space used for a container. Things that are not included currently are;

disk space used for log-files (if you use the json-file logging driver) - which can be quite a bit if your container generates a lot of logs, and log-rotation (max-file / max-size logging options) is not configured
volumes used by the container
disk space used for the container's configuration files (hostconfig.json, config.v2.json, hosts, hostname, resolv.conf) - although these files are small
memory written to disk (if swapping is enabled)
checkpoints (if you're using the experimental checkpoint/restore feature)