Coming up with 20% for a down payment helps you avoid having to buy private mortgage insurance (PMI). For down payments less than 20% of the purchase price, the mortgage lender will require you to buy PMI.
Why is the 20% important?
It is a measure to indicate that you have skin in the game, and that you are unlikely to default on your loan with so much money out of your own pockets. At the same time if you default on the loan, it is easier for the lender to recover 80% of the purchase price than 100% of the purchase price. Paying a bigger down payment generally lets the lender know that making a loan to you is less risky. They will also be able to afford you a lower interest loan seeing that you were able to put 20% down payment towards the purchasing your home.