To copy a file from a list of source paths in Column A to a corresponding list of destination paths in Column C, you would make a macro like this:
Dim i As Long, lastrow As Long
lastrow = Range("A" & Rows.Count).End(xlUp).Row
For i = 1 To lastrow
FileCopy Range("A" & i), Range("C" & i)
It's important to note the destination paths in Column C must be the full path; not just the desired new folder location. It's also important to note this macro copies the files from the source path to the destionation path. It doesn't move them. The original files will still exist in the source path.
Once you have your macro built, you can assign it to a button by clicking Insert > Form Control Button on your Developer Tab. You can even assign the macro to a shape, if you prefer.
The macro in this answer uses the native VBA FileCopy function, but you can also use the FSO CopyFile method. FSO stands for FileSystemObject and it allows you to control a whole suite of file properties. I highly recommend you take a look at our tutorial on the VBA FileSystemObject if this is something you're interested in.