Backbonding is a type of resonance. I can explain it through an example.
See, in compounds like BF3, the boron atom has an incomplete octet. The fluorine atom on its side has a lone pair which it can donate to boron. But, flurorine is also a very electronegative element. So, it also has a tendency to take back the electrons that it had donated to boron. This way, the lone pair of electrons keep jumping between fluorine and boron. This is called back bonding. This provides the lone pair of electrons more number of exchange positions (which simply means more space). As a result, the molecule becomes more stable.
However, back bonding is effective only when the size of the valence shell matches. In the case of BF3, both boron and fluorine have their valence electrons in 2p. But in BBr3, lone pair electrons are in 4p while valence electrons of Boron are in 2p. So, the size does not match. Also, electronegativity of the halogen decreases down the group. Hence, effectiveness of back bonding with Boron decreases down the halogen group.
						

							
As for acid strength, bf3, bbr3 etc. are lewis acids because the central atom is short of an electron pair. If the back bonding is effective, the shortage of electrons is somewhat compensated and the lewis acid character is decreased.
						

							
Thank you.
						

							
An empty P-orbital having species with incomplete octet eg. Be, B, C+ etc undergoes P(pi)-P(pi) back bonding when the adjacent atom contain a lone pair or negative charge.
						

							Back bonding is inversely prop to acidic st.,..........................................................................
						

							Acidic strength inversely proportion to back bonding or(back donation).so to decide the acidic strength we have to know about back bonding. BF3 TO BI3 extent of back bonding decrease so acidic strength BF3 to  BI3 increase. now question is how BF3 to BI3 extent of back bonding decrease?.  in BF3 boron and fluorin both has valence electron at 2p orbital and has same size and same energy level so when the lone pair of flourin goes to the vacant 2p orbital of boron to form back bond due to same size and energy level the extent of back bond in BF3 is more better than other halide so in  BF3 the due to better extent of back bonding it has no more space to accept the acidic electron so BF3 is low acidic With Respect To other Boron halides.
						

							
The size of boronand florine is comparrable,  so the vacant 2p orbital of boron is overlapped with filled 2p orbital of florine as Ppie Ppie bond or back bonding. But the size of halogens increases the filled p orbitals remains away from vacant p orbitals of boron remains deficient so acidic nature increases.