What does it mean to have "powerful" chakra? Tobi once stated that he (referring to Madara) was born with an especially strong chakra.

That is the only time we ever hear about the "power" of chakra! We know that one can have a lot of chakra, and we know he can learn to utilize his chakra efficiently. But what does "strong" chakra mean?

Does it make his techniques more powerful than other, less power chakra users? Does it mean that his YinYang balance is naturally stronger? Does it make him live longer?
I believe it's much like "The Force is strong with this one" :P

From Naruto wiki, we can learn that 


  Normal chakra is a form of energy all living individuals naturally
  produce to some degree. Contained in the "chakra coils" that mainly
  surround and connect to each chakra-producing organ, the energy
  circulates throughout the body in a network called the "chakra
  circulatory system" (similar to the cardiovascular system).


And, later in the same article, it is stated:


  Chakra is the resulting form of energy when two other forms of energy
  are mixed together. The two energies are referred to as "physical
  energy" and "spiritual energy". Physical energy is collected from the
  body's cells and can be increased through training, stimulants, and
  exercise. Spiritual energy is derived from the mind's consciousness
  (i.e. the soul) and can be increased through studying, meditation, and
  experience. Having these two energies become more powerful will
  in-turn make the created chakra more powerful. Therefore, practising a
  technique repeatedly will build-up experience, building up one's
  spiritual energy, and thus allowing more chakra to be created. As a
  result, the ninja is able to do that same technique with more power.
  This same cycle applies for physical energy, except this time, instead
  of doing things like meditation, the ninja could, say, do push-ups.


emphasis mine.

So, I think that saying that someone is born with "strong chakra" means that the physical part of that person's chakra (the one that he has from birth) is better... developed (or maybe advanced), comparing to other people. Whether this individual will further develop this natural...boon, depends on him. 

This estimation of chakra strength can also be different depending on who to compare with. For example, one can be compared with other members of the same clan, or shinobi of the same village, or maybe all shinobi in general.