The price of a bond is the present value of its future cashflows.
If we consider a coupon bond like a US goverment bond (T-Bond),
the cash flows look like

The current price of the bond is with discrete compounding,
and with continous compounding.
The interest rate is fixed,
which means that the term structure is flat.

Convexity measures the curvature of the approximation done
when using duration.
It is calculated as Simple Duration where
C(t) is the cashflow in period t