Invasive plants are those non-native plants that infest an ecosystem. Unlike normal weeds, which have evolved within a specific ecosystem, invasive plants generally do not have any natural enemies, so they grow out of control. They use up water and nutrients, pushing out local flora and fauna. Some, such as Scotch broom, can be poisonous to your pets.
Invasive plants are often introduced to your yard on purpose, by buying and planting something just because it "looks nice”. According to the UC Davis IPM (Integrated Pest Management) page: a 10,000 acre infestation of giant reed (Arundo donax) on the Santa Ana River in Orange County is estimated to use 57,000 acre feet more water per year than native vegetation. One group, PlantRight, has developed a list of invasive plants that should be avoided. Another group, Calflora, offers extensive lists (with photos) of plants that are invasives and plants that are under consideration as invasives.
Taking the time to plant species that are native to your area reduces water waste and prevents the disruption of the natural lifecycle of countless plants and animals.
I hope this information inspires you to grow more of your own food. You can ask your garden questions on my Home page.