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I'm implementing a UI where you can draw a box by clicking and dragging your mouse to select multiple items. Like selecting multiple files/folders:
Does this pattern have a name?
Questions about HCI
I've seen this referred to as:
In Axure this feature is named "select contained".
In my opinion, you could name this: "select contained items" or "Drag to select contained items".
Marquee select or area select.
This is also referred to as "rubberband selection", as a Google Image Search reveals. Incidentally, as you mention that you're developing a UI, the Qt UI framework has the QRubberBand class that can be used to implement this type of selection.
Required, but never shown