Sputum is the gross stuff that you cough up when you're sick and congested. Sputum is your saliva mixed with mucus from your lungs.
Examining a patient's sputum is one way for a doctor to tell if she might have an infection, rather than just a cold. A yellow or greenish color to the sputum someone coughs up is a sign of infection, while clear sputum usually means all is well. The word sputum shares a root with spew, the Latin verb spuere, "to spit."