I'm not really the best person to explain what DOSBox does exactly, but basically it creates an emulated DOS environment that tricks your computer into believing it's running DOS. So old games which require DOS can be run in this artificial DOS environment.
About which version to choose, just get the latest version for Windows. Mirrors are just different places to download it from so the servers don't get too busy, so you needn't worry about those too much.
Did that help you at all?
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