The following assumes a line frequency transformer.
All transformers provide dc isolation between isolated windings.
This capacitive coupling mechanism can carry high frequency noise on the input primary to the output secondary windings or vice versa. Isolation transformers are designed to minimize this coupling by construction that minimizes capacitive coupling, or by the use of shields, or both. Shields usually increases the capacitance between primary and secondary if the shield is not connected. However, by connecting the shield to the appropriate place, the noise can be diverted to a harmless place. Theoretically, you need one shield per system ground, although you can often get by with one less.