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To block something from flowing freely, typically water in a stream, river, etc. A noun or pronoun can be used between "dam" and "up." If we don't dam up the river, this rain will cause a flood.
dam something up
to erect a barrier in a river, stream, brook, etc. We are going to have to dam this stream up to make a pond for the cattle. Let's dam up this stream. Why is this river dammed up?