extension
Extra length, size, or time added onto something.
Extension means making something longer, bigger, or last for more time. When you need an extension on a homework assignment, you're asking for extra days to finish it. When someone adds an extension to their house, they're building new rooms to make it larger.
Think of how you extend your arm to reach something on a high shelf. An extension cord literally extends the reach of an electrical outlet, letting you plug in a lamp across the room.
In different contexts, extension means different things but always involves this idea of reaching further or lasting longer. A phone extension is an additional line connected to the main number. A file extension (like .pdf or .jpg) is the part added after the dot in a filename that tells the computer what kind of file it is. Hair extensions make someone's hair appear longer.
When you receive an extension on a project, you might feel relief because you have more time to do your best work instead of rushing through it.