Not necessarily. Closing a disc session makes the disc compatible with other computers and some consumer electronic devices, such as a CD or DVD player. However, not all discs need to be closed. You only need to close CD-R, DVD-R, and DVD+R discs. Rewritable discs (which end in RW) don't need to be closed, but they might not work in regular CD or DVD players either. In addition to this, discs that haven't been closed can still be used in other disc burners. However, they can't be used in most CD-ROM, DVD-ROM, or BD-ROM drives.
Some programs might offer to finalize your disc instead of closing the current session. A disc that has been finalized is complete. You can open files from the disc, but you can't add more files or save changes to existing files on the disc. When you burn a CD or DVD using Windows Explorer, the disc is not finalized. You can add more files later on as long as you have space on the disc. Some CD or DVD players can't play a CD or DVD that hasn't been finalized. This capability varies by the make and model of the CD or DVD player.
Mastered discs don't need to be closed because they are in a closed session already, which makes them compatible with other computers. Therefore, you will never see an option to close a session when burning a Mastered disc.
For more information, see Close or finalize a CD or DVD.