Misc. Objectives are the ones listed under "Miscellaneous" in your quest tracker. They can be as simple as going to talk to someone or investigating a certain area. Most of the time they point you in the direction of a side quest you haven't encountered yet. Some areas have a string of miscellaneous objectives instead of an actual quest, such as Vault 75.
If you want to complete this all in one go, here is a video of how to easily complete 50 objectives after joining The Brotherhood of Steel: