An "invasive plant" is usually defined as a non-native (or alien) species whose introduction causes or is likely to cause economic or environmental harm or harm to human and wildlife health. The worst invasives are often called "noxious" weeds or pests.
Invasive plants are introduced by many pathways. They can be deliberately planted in gardens or along roadsides and spread into surrounding habitats. They can be contaminants in crop seeds imported from other countries. Aquatic plant pests are often introduced into wetlands when people dump the contents of an aquarium into a pond. In several cases, seeds have been accidentally introduced from abroad when plant parts have been used as packing materials.
What can you do about invasive plants? Start by using native plants in your garden. Monitor exotic plants to be sure that they don't spread beyond your yard. Avoid non-native plants that produce fruits that are eaten, and thus widely dispersed, by wildlife. Check the Invasive Plant Finder to get a list of invasives for your state, and avoid introducing such plants into your local area.