A startup is a company designed to grow fast. Being newly founded does not in itself make a company a startup. Nor is it necessary for a startup to work on technology, or take venture funding, or have some sort of "exit." The only essential thing is growth. Everything else we associate with startups follows from growth.
A startup has to have the potential to grow really big. Most companies that are started don’t have this potential (restaurants, barbershops, plumbers…).
For a company to grow really big, it must (a) make something lots of people want, and (b) reach and serve all those people. Barbershops are doing fine in the (a) department. Almost everyone needs their hair cut. The problem for a barbershop, as for any retail establishment, is (b).
That space of ideas has been so thoroughly picked over that a startup generally has to work on something everyone else has overlooked. The obvious ones have been done already.
The growth of a startup usually has 3 phases. Initially there’s no/little growth, then there’s rapid growth, and then the growth starts to level off once you’ve saturated the market. This produces an S-curve.
A good growth rate during YC is 5-7% a week. If you can hit 10% a week you're doing exceptionally well. If you can only manage 1%, it's a sign you haven't yet figured out what you're doing.
We usually advise startups to pick a growth rate they think they can hit, and then just try to hit it every week. This is a good heuristic for making decisions (should I go to that conference, hire another programmer, spend time courting that big customer…).
Judging yourself by weekly growth doesn't mean you can look no more than a week ahead. Once you experience the pain of missing your target one week (it was the only thing that mattered, and you failed at it), you become interested in anything that could spare you such pain in the future.