Depends what you mean by "important". The bigger the hard drive is, the more stuff you can put on it without running out of space.
The space being used is important because it lets you know how much free space you have left to put more stuff on. Pretty basic.
The size of the hard drive goes directly towards your storage. The storage on your device dictates how much room you have for Photos, Music, Movies and programs/applications. While a large hard drive allows for more of those aforementioned things, it doesn't necessarily add to your device's performance. The Speed of the hard drive, along with Processor speed and amount of RAM (as well as speed of RAM) contribute to the overall performance of your device.
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