This is an important question and the names for these features have changed over the lifetime of Windows and Windows computers. But at this point hibernation is a mode where your computer can be turned off and everything that was in memory on your computer is saved to the hard drive.
If you have say 8 GB's of memory in your computer it will take up 8 GB's of storage on your hard drive to save everything that was in memory. When you turn the computer back on it will reload the memory from that saved hibernation file, It'll take 30 seconds to a minute to do that but when you start up the computer again it will be right where you left off.
Sleep mode on the other hand uses a little bit of power, Your computer is on but in a very low-power state and the contents of your computer's memory are saved in memory so when you start the computer back up it comes up immediately. On the other hand it doesn't actually turn the computer off so you don't get the full power savings of hibernation mode. You can choose which mode you want your computer to go into when you close the lid on the laptop or press the power button on your desktop computer.