"Seem to" means the same as "appear to." "Mind" means either to look after or care for something or someone ("Mind the gap") or to be distressed or worried ("I don't mind if you smoke"). Together, this would mean either "appear to care for" or "appear to be distressed by."
if you're watching tv while someone is reading a book and they don't say anything then they don't mind it which means it doesn't bother them.
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