The birds eat some of these seeds but others fall to the ground and germinate. Depending on the plant (and the location) this might be welcome or it might be a weed. That decision is up to me.
Garlic chives are notorious for seeding in so normally I would dead head them after blooming but I actually want a few more plants in the garden - I bought one and am letting it produce seeds.
This is a young columbine (Aquilegia canadensis). I have two varieties in my garden and I'm not sure which this will be. Columbine is a steady re-seeder but not aggressively so. It can be fun to see where these pop up and how they combine with other plants in unexpected and unplanned ways.
So when I'm out weeding I slow down and think - do I know what that is? and do I want more of it? Not weeding may be the right choice.