What's the equivalent to 'explorer .' (Windows) or 'open .' (Mac)?

xdg-open . will do what you want based on what is set as the default file manager, however since nautilus is the default I personally find it easier to autocomplete nautilus .

(Note that xdg-open is supposed to supercede gnome-open, as it's a Freedesktop.org solution that is cross-desktop and agreed upon instead of GNOME/KDE specific)

You may wish to give a chance to dolphin, which can be easily installed (if not already) by dropping the next line in a terminal:

sudo apt-get install dolphin

Dolphin is more like a "Finder" and it features the sliding effect in the vertical columns when opening folders and some other useful features.

After installind (or if already installed) drop the next in a terminal, or [Alt][F2] in order to invoke the "Run application" box in order to enter the next command:

dolphin

And enjoy.

A screenshot is placed here for you to see dolphin in action.