If you receive an Insufficient Disk Space error message during the installation process, this could be caused by a couple of things:

For starters, you'll need to check how much space you have available on your Machintosh HD.

To check your available disk space, open Finder, navigate to Go located at the top left corner of your computer screen, select Computer, and then right-click on your system drive (typically named "Macintosh HD", in the GIF below it is "Apple SSD") and select Get Info.

The amount of disk space that you have available is the 'Available' number – (minus) the 'Purgeable' number as shown below. 

If you have a lot of purgeable data, please see this article from Apple on how to remove it to clear up space.

If there is more than enough Available memory on your system drive and you are still getting an Insufficient Disk Space error message, you may need to temporarily turn off Time Machine.

To do so, go to your System Preferences, click on the Time Machine icon, and turn off 'Back-up Automatically'. 

After turning off Time Machine, try running the Mac installer once more (you can turn Time Machine back on once the installation is complete).

If you received this error more than once and are now trying to install to a different hard drive that has enough space, please follow the steps in this article for details on how to properly direct the installer to the new location.