There’s is a contraction of there is. It is correct to write, “There’s a hole in my bucket.” It is not correct to write, “There’s three holes in my bucket.” There’s only refers to one item. If you wanted to correct that sentence, you would write, “There are three holes in my bucket.”
There’s is also a contraction of there has. For example:
“There’s been fighting here for many years.”
“Throughout history there’s been military conflicts”
“There’s been extra work to do every since the head of the department changed”
Related: Now take it one step further with “Mastering There, Their, They’re.”
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