"Material Implication" refers to what seems like a paradox.
In "Propositional Calculus" [or "Sentential" Logic by some], given P, then (Q -> P) is true. Though this is logical under that system, the 'Q' seems odd to conclude true because it could technically be replaced by ANYTHING arbitrarily. If P = Chicken, let Q = Egg. This shows the historical circular reasoning often used by religion. You could assign P = Egg, then it would also be true that you might let Q = Chicken.
This 'paradox' is called "Material Implication".
In reality, it might be better to simply think of this meaning that for any given thing, something UNSPECIFIED can be conditionally the Q. It is actually the CONDITIONAL, not the 'Q', that the logic is asserting. But this is still controversial by some and why it was given a unique name. The 'material' being implied is that at least some 'Q' exists that implies a 'P'.