Here's an example:
"He said, 'I'm going to the store to buy some milk,' and then he left."
In this example, "I'm going to the store to buy some milk" is the inner quotation and is enclosed in single quotation marks. The entire sentence, "He said, 'I'm going to the store to buy some milk,' and then he left," is the outer quotation and is enclosed in double quotation marks.