It means to let the flowers stay on the plant until the flowers dry up and the seeds mature. Then you can either collect the seeds or let mother nature spread them around your garden. If you don't want it to happen you can trim off the flowers when they start to fade (often called "deadheading").

Also, by allowing tiny-flowered plants, like parsley, go to flower you provide food for very tiny, very valuable, non-stinging wasps.