The '-reversible' switch in lastile will give each point of every tile an index that stores what exact position they used to have in the one (too large to process without tiling) LAS/LAZ file they came from. This index is then carried through any number of LAStools processing steps on the tiles. This is only needed when at the end of these processing steps the original file (the one that was tiled) is supposed to be recreated with the processed results. This is accomplished by rerunning lastile with one complete set of the processed tiles as input and giving it the '-reverse_tiling' switch. This will then produce one output file with the points in the original order (minus those that might have been deleted during the processing steps on the tile.
You NEVER need the '-reversible' switch if you have no interest in eventually reconstructing the points in their original order into one file at the end of the tiling process.