One way to look at it is the notion of distribution (Fourier analysis):
The more precisely an object is located in space, the closer its spatial distribution resembles a Delta distribution (a very narrow peak).
Conversely, the less precisely an object is located in space, the more it looks like like a plane wave (the probability of finding it is the same everywhere in space).
To build a peak-like distribution using waves, one has to add to together a large amount of individual waves of different frequencies.
Conversely, a plane wave has only one specific frequency.
So, the more a wave-like object is narrowly located in space, the looser it is located in the frequency domain.
Conversely, the narrower the frequency distribution of of an object, the larger its spread in ordinary space (cf. a plane wave).
If one considers that the frequency of a wave is related to its momentum, then then the considerations above translate as:
"The more precise the location of a particle is in space, the more uncertainty there is regarding its momentum."
Since quantum mechanics obeys the Schrödinger equation, the considerations above apply to all particles (i.e. to matter in general).
Here is a formal description:
If quantum mechanics is correct, then it implies that the Heisenberg principle is true, conversely, if the Heisenberg principal was proven to be wrong, then it would prove wave functions not to be an accurate description of reality, Schrödinger's equation would be proven to be an inaccurate description of the evolution of a physical system and the whole of quantum mechanics would be invalidated by the same token.