${\mathrm{NH}}_3$ and ${\mathrm{BF}}_3$ combine readily because of the formation of:

${\mathrm{NH}}_3$ and ${\mathrm{BF}}_3$ combine readily because of the formation of a coordinate bond

While ${\mathrm{NH}}_3$ is a Lewis base, which is an electron-rich chemical, ${\mathrm{BF}}_3$ operates as a Lewis acid, which is an electron-deficient compound. Through a co-ordinate bond, ammonia may transfer its single pair of electrons from its ${\mathrm{sp}}^3$ hybrid orbital to the open p-orbital of ${\mathrm{BF}}_3$.