The strength of acidic character of boron trihalides depends upon $\mathrm{p\pi }-\mathrm{p\pi }$ back bonding.

In boron trihalides, $\mathrm{p\pi }-\mathrm{p\pi }$ -back bonding occurs due to empty orbital of boron and filled orbitals of halogens.

The $\mathrm{p\pi }-\mathrm{p\pi }$ back bonding is shown maximum by ${\mathrm{BF}}_3$, as the size of $\mathrm{B}$ and $\mathrm{F}$ are small and comparatively same. Due to this effect tendency of accepting lone-pair of electrons of boron decreases as size of halogen increases. The order of size of halogens are $\mathrm{F}<\mathrm{Cl}<\mathrm{Br}<\mathrm{I}$. Thus, acidic nature is in order

${\mathrm{BF}}_3<{\mathrm{BCl}}_3<{\mathrm{BBr}}_3<{\mathrm{BI}}_3$