Think of an excitation of the field. One of the "axioms" of quantum field theory is that the energy of an excitation is related to the inverse square of the wavelength. Don't ask me why, it's just like that. Think of UV radiation or X-rays, which are just light with a higher frequency and you know those radiation is more damaging to the human body than for example radio waves.
Now, are you familiar with Fourier decomposition?[1] It's the idea that all functions are the sum of a waves (sines and cosines). We do the same thing in quantum field theory, we have our quantum field and we write it as the sum of our elementary wavefunctions, which are called plane waves[2]. When you look at a wave packet[3], you can't really say what its wavelength is. Wavelength is not a local concept, as for example the height of the wave, but the wave differs from place to place, so it's impossible to give it just one wavelength! We don't have that problem with plane waves. Because they're the same all over the universe, they have a clear wavelength and thus a well-defined, unique energy. This concept, an excitation of a field with a well-defined energy (and thus a well-defined mass!) is what particle physicists call "a particle".
When a collision happens in a collider, we're actually preparing two plane waves and pointing them in the same direction. As they collide, the wavefunctions of the various fields become incredibly complex. We humans can only "see" excitations with a well-defined mass, or better yet, our detectors can only detect excitations with a well-defined mass. And thus instead of a complicated field, we see a mess of particles going in different directions and having different masses, energies and speeds.
Does that make it any clearer?
[1]: http://en.wikipedia.org/wiki/Fourier_series [2]: http://en.wikipedia.org/wiki/Plane_wave [3]: http://upload.wikimedia.org/wikipedia/commons/b/b0/Wave_pack...