Which letter in the spanish alphabet is silent and not pronounced when speaking spanish

That would be the letter "h".

All the other letters in the Spanish alphabet produce a certain sound (they are not silent/mute). However, when pronouncing a word that has the letter "h"--whether the word starts with "h" (hola) or has an "h" somewhere in between (ahí)--it's always going to be silent.

H. Hermano is pronounced "ermano"  for example.