To "process emotions" means to deal with and understand your feelings in a healthy way. It involves acknowledging and expressing your emotions, and finding ways to manage and cope with them effectively. Full definition
Yet for the sake of the students they lead, they are forced to help process the emotion and begin leading student athletes in the healing journey. (sportstarsmag.com)
It's a means of connection, and of helping our child process emotion. (attachmentparenting.org)