The convolution $C$ of a function $F$ with a function $G$ (of a parameter $t$) is defined as

$C(t)=\int_{-\infty}^t F(t-t')~G(t')~dt'$

In time resolved fluorescence it describes the effects of an IRF with finite width on the observed decay:

$Dec_{obs}(t)=\int_{-\infty}^t Dec(t-t')~IRF(t')~dt'$

where $Dec(t)$ is the unconvolved ('real') decay starting at a given time $t=0$