This is a sound that English speakers make in a few different situations:

• When something disappointing happens:

  Aw, my strap broke!

• When you see something cute:

  Aw, look at the baby holding her stuffed bunny!

• When someone does something sweetfor you:

  Aw, thank you! You shouldn't have! (When someone gives you a gift.)

The example above is probably closest to #3. When people pay you a compliment, you can start your response by saying "Aw":

Aw, thanks.