Having read through the Wikipedia page on cron, it is unclear to me when cron begins to execute the tasks I have defined in the crontab file. Is it during the boot process - or even at the end of it - or later? I am sure that they are executed when I login into the system (Linux Mint 17.3), however what happens if I do not? 
When do cron tasks begin to execute?
boot;cron;startup
The tasks defined in the various crontab files are executed by crond, which is started during boot by your init (whether that's sysvinit, systemd or Upstart). crond processes tasks as soon as it starts, so you'll see crontab-defined tasks potentially start executing before the system has finished booting.In any case crond will run tasks you've scheduled regardless of whether you're logged in or not. You can boot a system up without ever logging into it, and crond will still run the tasks that have been defined  this is typically the case on servers.The crond(8) manpage has all the details.