Infectious means able to be spread by infection, like a disease that spreads from one person to another. You'll be uncomfortable shaking Uncle Marvin's hand if you're worried that warts are infectious.
Something that's infectious spreads easily, like infectious cold germs that might be left on a door handle — anyone who touches it might get sick. If your mother tells you the cut on your knee looks infectious, you'd better go to the doctor. Some infectious things are good — like infectious laughter that gets the whole class giggling, or your friend's infectious good mood that makes you forget your cares.