Walt Whitman once said that a weed was a plant whose useful purpose has not yet been discovered. My dad, on the other hand, said that anything growing in the yard that was not grass was a weed. So basically it comes down to an anthropocentric value judgment. A weed is simply a plant growing where humans do not want it to at this moment. Often these plants are referred to as "invasive species." This term is defined as "a non-native species whose introduction does or is likely to cause economic or environmental harm or harm to human health."
Fennel, German ivy, pampas grass, teasel, yellow star thistle, milfoil, scotch broom, gorse, ice plant, dune grass, cheat grass, Klamath weed and bindweed are just of few of the noxious weeds that have found a nice and permanent home in the Bay Area. Last year, over $85 million was spent in California combating their myriad negative effects.
Weeds are hardy generalists. They are adapted to many different habitats. They thrive in disturbed areas like gardens and gravel parking lots and out-compete native plants. Extremely fast growing, weeds reproduce sexually and asexually. Flowers are mostly wind pollinated; the seeds are abundant and small, dispersing readily. And most importantly, these seeds can lay dormant for centuries.
They also reproduce asexually. With long taproots that break off easily, each piece generating a new plant. Or with runners like blackberries or underground stems like crabgrass. Many of them are armed and toxic, and some produce chemicals to inhibit the growth of nearby plants.
Many of our worst weeds are Eurasian in origin. They accompanied the European invasion of this continent. These plants had already spent thousands of years adapting to the severe alterations made to the environment by agrarian societies. In the New World the settlers cleared the primeval forests and plowed the native grasslands. These Eurasian weeds were "pre-adapted" to these severely disturbed habitats and took a firm hold. They have been expanding their range ever since.