There's no Save button in a Space. Every change you make saves automatically, and everyone with access to the Space sees it right away. Only change what you want everyone to see.
What you can edit in a Space
Layers: add data layers, group them, and change their filters, style, and visibility.
The portfolio layer: choose which projects show in the Space, and how they look.
Projects: edit each project's name, description, and workspace property values in the portfolio layer's Data Table, one at a time or several at once. You can also share and export projects from there.
Apps: add apps and change their settings.
Layouts: arrange panels and save layout tabs.
Space details, like the name, boundary, default template, and units: see Space Settings.
Anyone with at least Edit access to a Space can change it. Only Space admins can delete it.
What a Space can't do
Some project tools aren't available in a Space, like Use as template and Reset usage data. Their menu items are grayed out and say not available in a space. Open a project to use them.