If you measure the position of a particle with uncertainty delta-x, you have to use another particle with a wavelength smaller then that uncertainty.
So, if you try to measure the position of a particle as precise as possible, you'd need for example a photon with a very high frequency (small wavelength) but energy is = plancks constant * frequency.
Energy squared of a photon is the moment squared (einsteins formula).
This implies that you'd have to bombard the particle you try to measure the position of with a very high momentum photon.
But, if you bombard that particle with a high momentum particle, they will be both knocked in a random direction and the original momentum of that particle will have been changed.
Measuring the position of a particle necesarely results in an uncertain chance of momentum of that particle.
By using the distance time function, you'll be able to calculate the momentum the particle had between the two measuring points but you won't know the current momentum of that particle as measuring its position once again changed its momentum.
This shows intuitively that by measuring the position of a particle, you cannot measure the momentum at the same time with the same precision.
The uncertainty principle is more fundamental then the intuitive explanation above. It states that you cannot measure the momentum and position of a particle at the same time with very high precision. Measuring one changes the other.
There are many more relationships between variables of a physical system that we can't precisely measure at the same time.