The term "acidic" hydrogen of a molecule is used when the hydrogen is completely (easily) dissociated in solution, that is to say, it gives an "acidic solution", those are contained in Brönsted acids.
Brönsted acid is a molecular entity, or the corresponding chemical species, capable of yielding a proton by giving another entity or chemical species: the conjugate base.
A proton (hydrogen) is all the more acidic as the conjugate base after its departure is stable.
The acidic hydrogen of AMP is on the phosphate group.
I hope that makes sense.
