How the 21 Card Trick works
The site never knows your card. Your three answers push it to one spot: 11th in the pile.
Your column goes in the middle
The 21 cards are dealt in rows of three, which makes three columns of seven. When you name your column, it is picked up between the other two. Now your card is somewhere from 8th to 14th in the pile.
Each deal squeezes it
The pile is dealt again, three to a row. Cards 8 to 14 can only land in rows 3, 4 and 5. Your second answer puts your column in the middle again, so your card becomes 10th, 11th or 12th. Those all land in row 4.
Your third answer puts your column in the middle one last time. Seven cards sit on top of it, and your card is 4th in its column. 7 + 4 = 11. It is the 11th card, every time.
Do it for a friend
Deal 21 cards face up in rows of three. Ask which column holds their card, and pick that column up between the other two. Do that three times, and their card is 11th from the top.