'Include Develop settings in metadata inside JPEG, TIFF, PNG and PSD files' can serve two purposes:
1) A backup copy of the LR Develop settings.
2) Allows sending files to other Lightroom users for collaborative work so they can use your Develop settings. You can also do this using a DNG Export file so not really an advantage.
I do NOT use 'Include Develop settings in metadata...' since it can affect LR's performance if 'Automatically write changed into XMP' is also checked. Without that option checked you can use CTRL + S keys to update the file's metadata with any setting changes, but that's a PITA.
Alper Tonga wrote:
By checking it, I was expecting to see the effects of the applied Lr adjustments also in Bridge, but they can not be seen in Bridge.
If you open the file from Bridge using Adobe Camera Raw it will use the metadata Develop settings. Otherwise it simply shows the unprocessed original file data.