Breakfast nooks are not large rooms and you generally do not have extra room to expand your breakfast nook table by putting up a drop leaf. Drop leaves are extra leaves of a table that fold underneath or down at a ninety degree angle when not in use, but can be turned up to make your table larger. Most drop leaf breakfast tables are actually rolling breakfast carts.
The most popular style is a rectangular shaped cart with a bottom shelf where two stools can be stored when the cart is not in use. Typically there is a semi-circle leaf that will fold up when you roll the breakfast cart out to eat a meal. If you have a small breakfast nook or kitchen then this type of breakfast table with stools could be perfect for you because it does not have to take up room permanently. Instead, you can roll it out when you want to use it but store it against a wall or in a corner when you do not need it. Another advantage is that you can use this cart for purposes other than eating meals in your kitchen. You can use the cart to serve appetizers or drinks at a party, for example.
Just because most breakfast nooks are small and most people will not have room to make their breakfast table bigger, that does not mean that it is impossible. There are some breakfast tables with leaves.