To stifle is to cut off, hold back, or smother. You may stifle your cough if you don't want to interrupt a lecture or you may stifle the competition if you fear losing.
The verb stifle means “to choke, suffocate, drown.” It can describe a claustrophobic feeling, like getting smothered by kisses from your great aunt. At its most extreme, stifle means to kill by cutting off respiration. The metaphoric sense of stifle didn’t develop until well after the word was first recorded as a verb: "I can always tell — but never let on for fear of damaging his ego — that my boyfriend attempts to stifle tears during sappy parts of movies; his eyes well up at the corners and he’ll sniffle uncontrollably, claiming allergies."