The Toolbox is a piece of technology Nick Fury gave to Coulson after they defeated John Garrett. Fury then instructed Coulson to rebuild S.H.I.E.L.D., and that the Toolbox would help him do it. Fury then officially appointed Coulson as the new director.
Robert Gonzales had sent Bobbi and Mack undercover inside Coulson's version of S.H.I.E.L.D. in order to learn Coulson's secrets, and, after they learned about the Toolbox, Gonzales becomes convinced that Coulson and Fury's most dangerous secrets were kept in the Toolbox.
After Gonzales acquires the Toolbox, he realizes that he couldn't open it without destroying the information inside. Coulson later agreed to open the Toolbox for Gonzales if he agreed to help him on a mission to destroy a Hydra base.
After the mission was over, Coulson kept his promise to Gonzales and opened the Toolbox for him.
The Toolbox is encased in a pure vibranium shell and a DNA scanner designed to only let Coulson open it.