Home Blocks can be set up by both Teachers and Students, and are used as personal location which that user - and only that user - can teleport back to at any time. This allows users to be able to return to one specific point of their choosing very quickly, typically their home or base.
When a Home Block is placed, the user receives a message in the lower-left giving them the exact coordinates of their “Home”. This is where they will appear if they choose to teleport to their Home Block.
No one, not even Teachers, are allowed to have more than one Home Block at a time. If they try to place a second one, the first Home Block is immediately destroyed and they are informed of it in the lower-left.
Once their Home Block is placed, a Teacher can teleport to it at any time by clicking on the Home Button in the Teacher Menu (accessed by pressing the M key (version 1.7 >) or P key (version < 1.7)) under the Personal tab on the lower-right. They will appear on top of their Home Block upon doing so.
Students can also place and use Home Blocks. They must be either given to the student or placed in a chest for them to access, as they will not have access to it in the creative inventory.
It functions identically with a Student as it does with a Teacher, with two exceptions: Students teleport back to it by clicking the Home Button on their Student Menu (accessed by pressing the M key) as shown below, and Students can only destroy their own Home Blocks, while Teachers can destroy any Home Block.
Below is a video detailing the use of a Home Block
More information about the properties of the Home Block can be found here.