Annuals are plants that germinate from seed, grow, flower and set seed, so completing their lifecycle, within one year. Some, such as hairy bitter cress (Cardamine hirsuta), do this in a couple of weeks or a couple of months, so several generations can appear each year. Some will also grow, and even flower, during mild weather in winter.
Generally annuals produce lots of seeds, and as these can remain dormant in the ground for several years – “One year’s seeding means seven years weeding” – allowing weeds to flower and produce seeds, sets you up for many years of weeding!
As any plant “growing in the wrong place” is regarded as a weed, cultivated plants allowed to set seeds and produce lots of young plants where they’re not wanted can be regarded as “weeds”.
Many of our weedy species are naturally-occurring or wildflowers, so make sure these don’t produce seeds, unless you need or want more plants to cover larger areas of your garden.