Glue is what holds things together after they have been broken or split apart.
On athletic teams, a glue guy (or gal) is the one who, in the midst of adversity, will make sure that everyone sticks together.
In an corporate or professional setting, a glue guy (or gal) is the one who does the little (often unnoticed) things that help the team to succeed. But that isn’t all a glue person does.
Glue is an adhesive, so it also holds things (and teams) together.