In the Bronsted-Lowry definition, bases are proton acceptors.
To be a strong base, the substance needs to basically completely dissociate in an aqueous solution to give high "pH".
This is the balanced equation of what happens when NaH solid is placed into water:
NaH(aq) + H_2O(l) -> NaOH(aq) + H_2(g)
NaOH, as you may already know, is another very strong base that basically completely dissociates in an aqueous solution to form Na^+ and OH^- ions.
So, another way to write our equation is this:
NaH(aq) + H_2O(l) -> Na^+(aq) + OH^(-)(aq) + H_2(g)
The H^(-) in NaH accepts an H^+ ion from water to form H_2 gas, making it a Bronsted-Lowry base.
If we were going by the Arrhenius definition of acids and bases, NaH would be a base not because it dissociates to give OH^- directly from its chemical structure, but because it results in [OH^-] increasing upon dissociation.
This reaction happens with a large equilibrium constant, so we can say that NaH almost completely dissociates when placed into an aqueous solution. This makes it a strong base.
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You might be wondering why this reaction doesn't happen instead, which would make NaH an acid:
NaH(aq) + H_2O(l) -> Na^(-)(aq) + H_3O^+(aq)
This reaction doesn't happen because sodium has a lower electronegativity than hydrogen.
For example, HCl can form H_3O^+ and Cl^- ions in an aqueous solution.
HCl can do this because hydrogen is less electronegative than chlorine. Electrons is drawn toward chlorine. So, H^+ is easily pulled off of HCl to form H_3O^+.
But NaH has again, hydrogen more electronegative than hydrogen, so we more-or-less have Na^+ cation and a H^- anion, a consequence of electrons being drawn toward hydrogen.
So, instead of an H^+ adding onto water to form H_3O^+, the electrons go with H to form H^- ion and form H_2 gas by stealing an H^+ from water.