Second-order Greeks are nothing else but the second-order partial derivatives
of option prices with respect to different variables

Vanna: Vanna measures the movements of the delta with respect to small changes in implied volatility (1% change in implied volatility to be precise).
Alternatively, it can also be interpreted as the fluctuations of vega with respect to small changes in the underlying price.

Charm (or Delta Bleed): Charm measures delta’s sensitivity to a small movement in time to maturity (T).
In practical terms, it shows how the delta is going to change with the passage of time.

Vomma:  Vomma measures how Vega is going to change with respect to implied volatility and it is normally expressed
in order to quantify the influence on vega should the volatility oscillate by 1 point.

DvegaDtime:  DvegaDtime is the negative value of the partial derivative of vega in terms of time to maturity and it measures how fast vega is going to change with respect
to the time decay.

Reference : Options Greeks: Vanna, Charm, Vomma, DvegaDtime