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.
It is also technically possible that τὸν προκεχειρισμένον is functioning substantivally, and in this case χριστὸν is in apposition to προκεχειρισμένον. The one who was appointed is in fact Christ Jesus.
Part of the challenges of translating simple appositions is that can be difficult to do so with good English style. We often revert to commas or dashes, or something more inelegant such as “that is.”
NASB inverts the word order and says, “Jesus, the Christ appointed for you.” If word order is important, then this is not a good solution. The NLT has, “Jesus, your appointed Messiah.”
The ESV uses a comma: “that he may send the Christ appointed for you, Jesus.” The problem with this is that it is confusing when Scripture is read publicly. The unnatural pause required by the comma sounds awkward.
The NRSV is unnatural and also makes for poor public reading. “The Messiah appointed for you, that is, Jesus.”
The NIV is strange and also doubly translates the apposition with both punctuation and a word. “The Messiah, who has been appointed for you—even Jesus.” The use of “even” makes it sound as if Peter was surprised that “even Jesus” could be appointed.
The NET also doubly translates, using both punctuation and an added phrase. “the Messiah appointed for you—that is, Jesus.”
The point is that the construction can be difficult to move smoothly into English, especially when you are considering the public reading of the text. I am certainly not in favor of double translation, especially when it results in poor English. While the ESV is awkward, it seems to be the best solution in this verse.