Symptoms can only be described by the person feeling them. If you are having pain, no one knows unless you tell them. It's the same with dizziness, numbness, lightheadedness, fatigue, vision disturbances, ringing in your ears and a whole host of other feelings that anyone not in your body is going to know about unless you describe it.
That doesn't mean other people don't notice when you don't feel well. If your face is pale or you are unstable when you walk or you are sweating, then you are showing signs. Signs are just what they sound like: indicators of a problem. They also include breathing rate, heart rate, oxygen saturation, etc.
People read signs all the time. Need to go to the 4th floor? Push the elevator button next to the sign with the "4" on it. Need to take the freeway north? Read the signs to find the right ramp.
Medical signs aren't always read with the eyes. Sometimes we read signs by touch or by listening. Some of the most common signs we assess in the medical field are the skin signs: color, temperature and moisture. People who are pale, cool and moist are usually feeling pretty bad.
Parents read signs from the day they bring their first child home. The baby's crying, maybe he needs to be fed.
Sometimes, signs indicate symptoms (like how a crying baby may be a hungry baby). Is your daughter scratching her arm (sign)? She must feel itchy (symptom).
Most medical conditions have both signs and symptoms that help identify what is wrong. Heart attack victims will often complain of symptoms -- pain or pressure in the chest and arm -- and show signs -- clutching the arm or chest, pale face, sweating, abnormal heart rate and high blood pressure, for example.
Often at About.com First Aid, just to keep things uncomplicated, I'll use the term symptom for everything. The most important thing to remember is to pay attention to both symptoms and signs when you're concerned about a possible emergency.