Why is aniline soluble in aqueous hydrochloric acid whereas acetanilide is not?

Because aniline is an amine, which are basic, but acetanilide is an amide, which are not. The reason for the latter is that the non-bonding pair of electrons on the NH2 in an amide group is delocalized into the C=O (you can draw a resonance structure H2N=C(R)-O with a positive charge on the N and a negative on the O). That resonance form means that the non-bonding electrons on N are much less available for binding to H+ from an acid. It also explains why the amide group is flat (sp2), rather than pyramidal (sp3).