There is no direct equivalent, system32 is just a collection of libraries, exes, and confs.

Some of what others have said is accurate, but to explain a bit further:

Longer explanation:

The basics:

• /bin - base level executables, ls, mv, things like that
• /sbin - super-level-only (root) executables, parted, reboot, etc
• /lib - Somewhat self-explanatory, holds libraries, lots of things put their libs here, including linux kernel modules, /lib/modules/*, similar to system32's function of holding critical libraries
• /etc - Configuration lives here, generally speaking, /etc/<application name> can point you in the right direction, typically requires super-user (root) to edit
• /usr - "User installed" software, which can be a murky definition in today's world, but lots of stuff ends up here for installed software, manuals, icon files, executables

Bonus:

• /opt - A special location, generally third-party, bundled-style software likes to use this, Java for instance, but historically some admins use it as the "company location", meaning internally developed software would live there.
• /srv - Largely subjective, but myself and others I know use it for partitions that are outside the primary disk, for instance we use /srv/db for database volumes, /srv/www for web-data volumes, /srv/Media for large-file storage, etc, etc

For completeness:

• /home - You'll find your user directories here, personally, this is my directory I backup, I don't carry much more with me on most systems.
• /var - "Variable data", basically meaning any data that will likely grow over time, eg: /var/log