Here is a non mathematical fast track explanation of convolution
Convolution requires two signals. The audio and the impulse signal. The convolution process take these two signals and produces a third new audio signal. The process requires a great deal of calculation the length of time depends on how long the impulse and audio signal are.
The impulse can be almost any type of audio signal. The key thing to remember is that is the impulse and the audio signal must have something in common to hear a result. For example if the audio signal has only a sine tone at middle C and the impulse has a sine tone at C# the result is no signal - just the noise floor of the audio signal
The impulse can be any type of signal but there are a couple of classifications.
1) filter (not moving static)
2) Echoes
3) Reverb Impulse
4) timbral filter
The filter impulse can be any conceivable type of fixed equalization (not a moving analog synth filter). These impulses sound like ticks and in effect have all the audio frequencies from 0-22KHz (44.1 Sampling Rate) so they always have something in common with the audio signal. They have everything in common the only difference is that the frequencies (or harmonics) of the impulse are all not at the same amplitude so the convolution process boost or reduces the gain which depends entirely on the make up of the impulse.
A tick (a single amplitude sample) in a sea of zeros before and after this tick will result in an echo of the entire audio signal. An impulse with such a tick at sample 1 then at sample 44100 but -6 db down and then another sample at 88200 but -12 db down will result in an an audio signal with the original sound and two echoes 1 second apart. The original signal then the original signal delayed 1 second but mixed in at -6 db original then another original signal delayed 2 seconds but mixed in at -12 db. This type of echo effect is heard in some manner in many digital effects units.
The Reverb Impulse class of impulses are noise like signals that decay over time. The advantage of a noise like signal is that is has all the harmonics in the audio spectrum. So regardless of whatever the audio signal has in it harmonic make up it it will always have something in common with the impulse signal. If the audio signal has a harmonic at middle C the reverb impulse also has that harmonic but it will last much longer than the audio signal tone (should be wetter sounding !) then the results will be a middle C tone that slowly decays over time (reverberates). The length of the delay at middle C depends on the characteristics of the reverb impulse.
The timbral filter impulses are very complex impulses designed to transform the timbre of the source audio material. There are no examples that I am aware of these type of tones on the internet. They take a great deal of time to create. What I personally do is sell the results not the impulses. There are result examples posted on the internet are samples from Drone Archeology, the Percussion Wall (some of the loops in 02pwall.mp3) and the Electro-Acoustic Modelling Examples of New Orleans;The Delta grooves