A beautiful smooth lawn gets most of its good looks from the fact that it is smooth and level with no weeds sticking up above the turf. You have probably mowed your lawn before only to have dandelions popping up above the grass a day later making it look like you need to mow already.
A weed free lawn holds its good looks for several days if the grass is a monoculture with uniform growing heights.
Weeds are really just one type of plant that we have decided shouldn't be growing in one particular place. It's your point of view as to what makes a weed a weed.
Some weed-type plants are invasive and fast growing. Their growth habit overtakes our cultivated turf plants, depriving them of food and water. Other weeds are extremely noxious and cause problems for humans if they get close them.
In the lawn, the most common weeds are just a nuisance. Most don't cause skin reactions or breathing difficulties, they just don't look good.
What they're also telling us is that the lawn isn't as healthy as it should be. Turf grasses today are so adept at growing into thick masses, that if maintained properly, weeds are not a problem. It is when the lawn isn't as healthy as it could be that we see weeds becoming a problem for the lawn.