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.
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.