Your draft
Every change in the customizer is saved right away as your draft for the public theme. The draft:
- is visible only to you, in the customizer's preview (and in previews you open in a new tab);
- never changes what visitors or other administrators see;
- stays until you publish or discard it, even if you close the customizer, log out, or come back from another computer.

Each person has their own draft, and a draft holds only the settings that person changed: the others follow the published settings. Two people can try ideas on the same site without affecting each other.
Drafts belong to a theme. If you switch the public theme, your draft for the previous theme waits until you switch back.
Publishing
Click Publish. The customizer saves the theme's settings exactly as Configure Theme would, with your changes, and deletes your draft. The page shows Your changes are published. and visitors see the new settings on their next page view. An image you replaced is deleted, as on Configure Theme, unless another setting still shows it.
If a setting is not accepted, nothing is published: the customizer opens again with the problem listed at the top and marked on its field.
Discarding
Click Discard changes and confirm. Your draft is deleted, with any images you uploaded for it, and the form returns to the published settings. Discarding is only available while you have unpublished changes.
Draft and Configure Theme
The Configure Theme page (Appearance › Themes › Configure Theme) always shows the published settings, not your draft. Saving there publishes its own form. Your draft stays as it was: the settings you changed in the customizer still show in your preview, and publishing them later applies them over what was saved.