I cant understand what this DRC error means.
Especially I do not understand this box. Does it mean that the Soldermask will cover part of the pad? How to correct it?
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It's due to the fact that your reference designator font is "proportional", not "vector".
Proportional fonts in eagle are collision detected with a rectangular box which is what the DRC is erroring about - the bounding box of the ref-des intersects the stop mask.
Vector font converts to a series of lines so collision detects the actual lines rather than the bounding box.
I'd recommend always using vector font. In fact there is a setting in the layout editor options for converting all fonts to vector.