Basically, it's trying to hold back any crying in a situation. The simple fact is that tears are often seen as a sign of weakness. Therefore characters hold them back to try to be strong, either to appear so as an example to others or because it's expected of certain people. Now often people will fail at this, because the grief is too strong for them to hold back, or because they reach a breaking point. Other times the grief may manifest in other ways if it's held in too long. Sometimes the grief can eventually be let out through Manly Tears. Contrast Ocular Gushers, Unable to Cry.