The definition of a weed is a plant growing in an undesirable location or situation - basically a plant growing in the wrong place. They are usually fast growing and compete with your plants or lawns for light, nutrients, space and water so if the weed is a menace, get rid of it, it's pretty simple!
Ralph Waldo Emerson describes a weed "as a plant whose virtues remain undiscovered" and I totally agree with him! When something springs up in my garden and I can't identify as a 'weed', I like to let it grow to see what it might be and give it a chance to prove its worth.
Many people will just see a weed or a pop up plant and get rid of it but sometimes if you just give it a chance they can be a fantastic new addition to your garden.
I have had many that I have kept over the years and one of the newest ones is a Watermelon that we had pop up in our lawn and although my husband's was annoyed that I wanted to keep it, I convinced him to let it grow so now we have a few small watermelons on the vine!
This Watermelon is an old fashioned heavily seeded variety that my mother had given to us and our kids sat outside enjoying with juice dribbling down their chins whilst spitting out seeds all over the place in the Summer - as you do - and that's the way we got this 'weed' Watermelon in our lawn!
I was surprised that it is still going strong because the usual season for Watermelon is Summer and in SE QLD it's just started to get cold so we'll have to wait and see if any of them get to full size or die off over the colder months.