Apposition is when you want to use a substantive to qualify another substantive. One way to do this is by putting the second substantive in the same case as the first.
In Acts 3, Peter calls for repentance so that “times of refreshing may come from the presence of the Lord, and that he may send the one appointed for you, Christ Jesus (τὸν προκεχειρισμένον ὑμῖν χριστὸν Ἰησοῦν).”
What does τόν modify? If it goes with χριστὸν (NA28 uses lower case), then we have the construction, article (τόν) – modifier (προκεχειρισμένον ὑμῖν ) – noun (χριστόν), and Ἰησοῦν is in apposition to χριστόν. The Christ (Messiah) who was appointed is in fact Jesus.