The theory is that competition as a cornerstone trait in a Capitalist system that rewards companies, products and services that innovate - making what they're selling of greater value to the consumer. Going back to the "Invisible Hand" theory: Here's a formal definition so we're all on the same page:
http://en.wikipedia.org/wiki/CompetitionCo-operative competition
Further information: coopetition
Co-operative competition is based upon promoting mutual survival - “everyone wins”. Adam Smith’s “invisible hand” is a process where individuals compete to improve their level of happiness but compete in a cooperative manner through peaceful exchange and without violating other people. Cooperative competition focuses individuals/groups/organisms against the environment.<3>
Wiki makes a distinction between cooperative competition and a more destructive type:
Destructive competition
Destructive competition seeks to benefit an individual/group/organism by damaging and/or eliminating competing individuals, groups and/or organisms; it opposes the desire for mutual survival. It is “winner takes all”, the rationale being that the challenge is a zero-sum game; the success of one group is dependent on the failure of the other competing groups. Destructive competition tends to promote fear, a "strike-first" mentality and embraces certain forms of trespass.<3>
When you hear free marketeers spouting the merits of Capitalism, they will refer to the Invisible Hand in the former. But I can't think of a single modern example that puts that description into play - where the best is also widely accessible and the providers are duly rewarded.
You rarely hear people sell capitalism by the latter definition of competition, for reasons that are even obvious to them. But I think we can cite plenty of real-world examples with that theory in-play.