I am about to erase everything off of my hard drive and install Linux Mint I'm doing this on a Dell laptop, there is a Dell utility partition that I have never used... I have seen these on other laptops by other manufacturers as well. What are they used for and what are the consequences for overwriting them?
The hidden partition will probably contain an image of a Windows install as others have suggested, but it may also contain a collection of diagnostic utilities provided by Dell. These can check the health of a variety of components in the system (eg. disk) and provide you with a list of error codes to supply to Dell when you report a problem.
I would recommend that you boot into the utilities partition and see what is available.
If you never intend to use Windows or ask Dell for support, then go ahead and trash it.
It is often an image of your Windows OS with all the drivers, etc needed for that specific machine. Oh, and of course all the bloatware they like to throw in. Usually you can hold down a certain sequence at boot-time for their custom boot loader to jump to that and then a small utility restores the image to the main partition.
TL;DR: If you have no intent of ever going back to Windows, feel free to nuke it all.
Some laptop BIOSes (e.g. Acer TravelMate 5720 with older firmware) will change the partition ID of some arbitrary partition to the value it expects the recovery partition to have even if the recovery partition is no longer there, which can render the system unbootable if it is the boot partition which is modified in this manner. You should experiment with this a bit before installing, to be sure that this won't happen to you.