I used Teamwork Projects extensively at my previous company. I also consulted with other companies to implement the software as a certified Teamwork Expert. In Teamwork, we managed every single thing that needed to be done.
We used to say "if it's not in Teamwork, it didn't happen."
Teamwork was useful for planning, communicating and collaborating, time tracking, and reporting.
A project manager would put everything that needed to be done in Teamwork and assign it out. This could include time estimates, dates, etc. Then every employee can pull up Teamwork and see exactly what they need to do.
As we are working on tasks we are constantly updating our tasks in Teamwork by posting comments, uploading files, and tracking time. This way management instantly knows the status of every task and project being done in the company.
Because we tracked our time in Teamwork, we could look over time and see how effective we were being. Time is typically your biggest cost. I found it extremely useful to figure out what we should be charging clients (even if you aren't charging by the hour, you still need to know).