I'll try to be as descriptive as possible.
I just bought an Acer Aspire one Cloud-book 14 for th specific reason as to run Linux Mint. I downloaded Linux mint 18.1 to a usb stick. I rearranged my BIOS to run my us stick first. everything as fine. It loaded a page that had 4 options. It was something similar to the following:

1. Linux Mint 18.1 64bit Cinnamon
2. Linux Mint 18.1 (Compatibility mode)
3. Linux 18.1 (manufacturer)
4. ? I cant remember.

I loaded the first option. It worked just fine. I set up a few things and even downloaded a few apps. I am Brand New to Linux but I fell in love with my new OS.
Now that brings me to the issue. When i was done fiddling around with my new machine, i shut it off. Later when i rebooted, i found that none of my changes had saved. I don't think I'm running a Virtual-box, but I'm not sure either. I've seen other posts online about the same issue, but no real answers were given. Instead of just telling me how to fix the issue, I'd like to learn about where I went wrong and understand how to fix it.
Thanks in advanced for any information.

Did you actually install Mint? If you just run it as a live disc, you can't make changes. If you really like it, take the plunge and choose the option to install it to your hard drive.

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looks like all you did was run it off of your USB Stick?
Because nothing in that list, nor in your explanation states anything about an install having been done. Because, again, one can still download and install apps onto the USB Stick until it runs out of room.

On my desktop environment there's an icon that says install Linux mint. I clicked on that and walked through the steps. When I was finished, I rebooted my cloudbook but to no avail. I'll try it again and see if there are any changes. I'll update this thread and thanks for the feedback.

This one?
did you make sure you installed grub to the MBR, or is it using IEF , you said you made changes to your BIOS, or was that just so you put USB Port hdd as first on boot list?

if it is not booting without your usb stick in it then, Huston we have a problem.

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The only changes I made to the Bios was to rearrange the order of the boot so that instead of windows running, my USB would run instead. As far as the grub in my MBR is concerned, sadly, I don't know what that means.

oh you are a NewwwwwwwwBe yes yes yes, Grub is your boot loader and the MBR is where it is installed to on your hard drive. you know hard drive yes?
sounds like we might have to go thorough a step by step of what you did to get yourself into this mess.

Just unplug your usb stick. If your OS doesn't work without your usb stick plugged in, then it means that you didn't install it.

Lol, yes I know hard drive. I looked up MBR. Makes sense. I was unaware that I needed to install grub to my MBR.

I'd suggest doing everything all over again and make sure you have it format where you are going to install it again, to get rid of whatever is there, just in case, else you'll have more problems. then when it gets to that part where it asks you about grub have it install it onto your /dev/sda , then reboot, pull your usb stick then let us know how that went.

I'm installing Linux again using the icon on my DE. I'm waiting to see if it asks me for input on grub currently. I'll update as soon as possible.

Ok, I did everything over again and tried to boot without my USB stick. Black screen that said no OS was all I got. So, I've decided to re-download Linux mint to an SD card. And try it all over again from scratch. Any useful tips, tricks or pointers would be fantastic

You mention using windows but not which version of windows. If you have windows 8 or newer pre-installed, it is in all likelihood using UEFI. If that is the case, you must install Mint using UEFI or you will not be able to boot one of the systems. If you are using UEFI, you do not want to install Grub to the MBR. You install the Grub files to the FAT32 EFI partition. See the link below which discusses doing this with windows/Ubuntu. Mint will have the same options as Ubuntu.

https://help.ubuntu.com/community/UEFI

Thanks for mentioning that. I had wondered what UEFI was. My laptop had windows 10 preinstalled.

shouldn't any good self respecting Installer pick that up now days?
I've only did UEFI once installed a Linux Distro UEFI for someone else, and I do remember the installer (slackware) pick it up and booted UEFI and installed accordingly.