The acid deprotonates in aqueous solution, and the negative ions induce nucleophilic attack on the positively-charged metal ions, removing metal ions from the metal and combining with them to form a salt.
The protons that dissociated into solution quite often recombine with each other to form diatomic hydrogen, which bubbles out of the solution as a gas.
This process of removing metal ions from the metal itself to be recombined into a salt with the original acid is called corrosion.
So, in a nutshell, the acid breaks down into ions, eats away bits of metal atoms from the original metal mass, combines into salt with the acid, and the hydrogen from the acid recombines to hydrogen gas, which bubbles out of the solution.
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