The base form is "설레다", and it's one of ways to express our feelings in Korean. We use this kind of expressions when we are going to expect something good or exciting will happen soon in front of us. This feelings makes us feel happy, nerveous and sometimes sweat a bit.
Also, "설레" without "다" could be an interrogative form of "설레다" or a response to your feelings in a quite informal way. Usually this word goes with several words together like "가슴이 설레다" "마음이 설레다" "마음이 설레고 가슴이 뛰다".
here are some examples.
B: 응 생각만해도 가슴이 설레. 그녀을 다시 만날수있다니.10년 만이잖아..
A: 내일 첫출근이라면서?
B: 응 가슴도 설레고 긴장되서 어제 한숨도 못잤어.