When in doubt, google is your friend. Googling for ''<term> definition' will usually pick up the right answer. But for the two you mentioned...
Cardio: short for cardiovascular. By definition, this is any exercise that is done to increase your heart rate (as opposed to weight lifting which is done to increase your strength); by usage, this is exercise that is done to burn calories. Examples are: running, swimming, biking, stair-climbing, most sports, etc.
So when someone says they do 30 minutes of cardio on their off days, they're saying they run, bike, swim, etc, for 30 minutes.
HIIT: High Intensity Interval Training. The basic idea is instead of (as an example) running for 30 minutes at a moderate pace, you run for 15 minutes, alternating between a moderate pace and maximum effort. See here for more:
http://www.musclemedia.com/training/hiit.asp
Not everyone believes HIIT works.