Your catalogue is a single .lumcat file holding every photo record, keyword, collection and develop setting. Its thumbnails live in a companion .lumthm file alongside it.
New Catalogue… — create a fresh, empty catalogue.
Open Catalogue… (⇧⌘O) — switch to a different .lumcat file.
Open Recent — jump back to a recently-used catalogue.
Optimize Catalogue… — opens Catalog Settings, where you can compact and tidy the database for speed.
Rename Catalogue… — renames the catalogue and its companion thumbnail file together, so the two never lose track of each other.
Import Photos and Video… (⇧⌘I) — bring new files into the catalogue from a card, folder or drive.
Import from Another Catalogue… — the Lightroom migration wizard. See Import from Lightroom for the full walkthrough.
Auto Import — turn on Enable Auto Import to have files dropped into a watched folder added to the catalogue automatically; Auto Import Settings… sets the watched folder and destination.
Export… (⇧⌘E) — render the selected photos to JPEG, TIFF and more, with control over size, quality, naming, metadata and watermarking. See Export & print.
Export with Previous (⌥⇧⌘E) — re-run the last export with the exact same settings, no dialog.
Printer… (⌘P) — choose the printer and open its options.
Print (⌥⌘P) — print the current layout. These switch to the Print module first.
Coming soon
The following File-menu items appear for familiarity with Lightroom but aren't active yet: Import a Photoshop Elements Catalogue…, Start Tethered Capture… (start tethering here — for now, use the Capture module), Import Develop Profiles and Presets…, Export with Preset, Export as Catalogue…, Email Photo…, Print Settings…, Set Quick Collection as Target, Library Filters presets, and the Plug-in Manager / Plug-in Extras.