In larger districts like the one where I work, keeping track of shared documents can not only be confusing, but also problematic if an owner leaves or even simply moves or deletes a document. Team Drives, first introduced in March of 2017, help groups manage access to documents that are important to whole teams of users. Where an individual's Google Drive is solely managed by a user, and all of the documents created and stored there can be given permissions determined by that user, Team Drives make it easy for anyone in the team to manage access to files. Every member of the team has set permissions based on who needs to edit, comment, view, reorganize or even remove files.
It's important to note that, by default, all members within a Team Drive can automatically see ALL of the same files, regardless of who adds or reorganizes them. This can be extremely helpful when trying to "efficify" shared documents, but could also prove to be problematic when the wrong documents are shared. Documents containing student data or sensitive information should NOTE be stored in Team Drives (or anywhere in Google, actually . . . ).
The most critical difference between Drive and Team Drives is that, unlike files in a user's own Google Drive, files in Team Drive belong to everyone in the team instead of a single individual. This is great for documentation of critical pieces of workflow, especially if members of the team ever leave. When created or moved to Team Drives, files stay there so that the team can continue to share information and documents.
Once the Team Drive is established, anyone with "Full access" can manage the other team members and their privileges within the Drive. If it is not essential for a user to be able to edit files, for example, his or her permissions can be changed to "View access" only. This would be useful if there is concern that someone might be able to modify or edit an important template, for example.
One final observation about Team Drives, and something to consider when and if you decide to implement them. If you create or are a member of more than one Team, and you wish to move files between Drives, you must have "Full access" privileges to the original Team Drive and at least have "edit" access to the destination Drive. The only to move a file if someone else is the owner is to ask them to do it for you.
The moral of the story is to give some careful consideration as to what you will store in Team Drives, and who will have what kind of access to it . . . all of it. Remember: everything in the Team Drive belongs to the Team.