I have a necklace that is a cross charm with Jesus Christ on the cross but on both sides. What's the meaning of this symbol?
A double-sided crucifix has the same religious significance as a single-sided one. It is an artistic device that enables the image of Jesus to been seen from two sides. This is particularly useful in the case of a necklace, where the jewelry may rotate toward the skin, so that the face of crucifix would not be seen otherwise. This tradition is also used for altar pieces, as in the above photo, so that viewers will see the image of Jesus whether they look from the front or the rear of the crucifix.
For those who are worried about the word "charm," I'm sure the OP does not mean this in the sense of a magical device but as simply "a small ornament worn on a bracelet or chain".
Your word description is insufficient to convey what this bit of jewellery looks like. You refer to it as "a charm" which is a bit alarming, as it indicates something of superstitious value. However, if you read in the Bible book of Mark, chapter 16 verses 27 and 28, you will note that two other crosses were on each side of Jesus' cross. The men on those crosses were called thieves, and one was on Jesus' right, and the other on his left. Jesus was in the middle.
Could this be what you are referring to? Without a photograph of the piece of jewellery, we really need a much more detailed verbal description, so if you could add more, that would be helpful.