Snobby people think they're better than others. A snobby club might only allow members who dress a certain way or attend a certain school, excluding everyone else.
Some snobby people are wealthy and believe that those who have less are inferior, while other snobby folks are smart and well-educated, and look down on people who are uneducated. Snobby is an informal word that describes a snob, which originally meant "a shoemaker or a shoemaker's apprentice." From that meaning it evolved through "lowly person" to "lowly person imitating a social superior" and finally "person who despises those considered inferior."