Deep pocket sheets are fitted sheets with deeper corners designed to fit thicker mattresses. The pockets, or fitted corners, and the sides of the sheet that cover the edges of the mattress are longer than normal.
Some mattresses are thicker than normal for better cushioning. Traditional fitted sheets often don't stretch down far enough to fit easily under the mattress. The corners are more likely to pop off when using regular fitted sheets. The deep pocket sheets fit down and under a thicker mattress better in the corners. The packaging should say "deep pocket" if the sheet is designed to fit around the thicker mattress sizes.