To expectorate is to force liquid out of your mouth — in plain English, to spit. Most often it means coughing something up from your chest and spitting it out, but it can just mean spitting. It is a strange word socially. It is far too formal for ordinary use: nobody watching a baseball player says 'he expectorated'. You meet it in exactly two places. First, medicine: a doctor asks whether you can expectorate, meaning can you bring the phlegm up. Second, public signs and rules — the old-fashioned 'Do not expectorate' on a bus or in a hospital, where the writer wants to sound official and, perhaps, less rude than writing 'no spitting'. That is the joke inside the word: it is a polite dressing-gown put over a very ordinary, slightly disgusting act. In real life, say 'spit', or 'cough it up'.

吐痰、把痰咳出來（正式用語）。日常說 spit 就好；expectorate 是醫生問診或告示牌上「禁止隨地吐痰」那種正式講法。