to take something out of the ground by digging

It's time we dug up those potatoes. 现在我们该把那些土豆挖出来了。

to break the ground or to make a hole in it with a tool, machine, etc.

They're digging up the road outside to fix a faulty water main. 为了维修出问题的供水总管，他们在挖外面的路。

to discover secret or forgotten facts by searching very carefully

I've been doing some research on our family history and I've dug up some interesting information. 我一直在研究我的家史，并且挖掘出了一些有趣的信息。

She's one of those reporters who's always trying to dig up dirt on (= unpleasant private details about) celebrities. 她是一贯热衷于挖掘名人隐私的记者之一。