In general, this processing should be avoided if you are not mixing your own pieces. Each of these can improve your sound, but are difficult or impossible to un-do if applied poorly. Some microphone pre-amps have these capabilities built-in, so that one can get a smoother, cleaner sound, and if used well, they are effective tools.
Compression will reduce the overall dynamic range of your audio signal, that is to say, the difference between the quiet and loud sounds will not be as great. One can apply different ratios of compression, so that, for instance, with a 4:1 ratio, as the input sound gets louder by 4 dB, the compressor only allows the output to increase by 1 dB. This effectively makes the signal quieter overall, but because the peaks are not as high, one can apply “make-up gain” so that the average level of the audio is higher.
Most compressors have controls for threshold, which adjusts the level at which compression is applied, signals beneath the threshold value are not affected. Many newer units automatically set the attack and release values, but if they can be tweaked manually, these controls adjust the rate at which the compressor begins working once the signal exceeds the threshold value, and then returns to no compression when the signal drops below the threshold.
Compression is very helpful with certain sounds. Voices in particular can often benefit from some of this “smoothing”. But if it is over-done, the signal can sound very unnatural, squashed or dull, or one might hear artifacts of the process like “pumping” where the audio or background ambience gets louder and softer in a weird way. Also, as the average level is brought up, some sounds that are normally in the background, like mouth noises and breathing, may seem too loud. Find a happy medium, too much compression can sound lifeless and dull, but too much dynamic range can make it hard to hear quieter parts of the recording. For compressing a voice track, try starting with a 4:1 ratio and adjust the threshold so that 4-6 dB of gain-reduction occurs during peaks, then tweak from there.
Limiting is a variation of compression, where a very extreme ratio is applied, so that no increase in volume is allowed past the defined threshold. This works great with certain processors, but be careful, anyone who has used the built-in limiter on a tape deck knows that it can distort the audio, or give an unnatural sound, if too much level is fed into it. Despite the dangers, a well-tweaked limiter can be an excellent tool on individual tracks or on complete mixes, especially when recording to digital devices, which do not tolerate "overs" well.
DSP-based limiters, like the TC Finalizer, or the Waves L1 plug-in are especially effective because they can do “look-ahead limiting,” which allows the devices to adjust their settings by adding a tiny delay and analyzing a few samples, in effect, looking into the future by a few milliseconds and deciding how much gain to reduce.
Expanders are reverse compressors, they increase the dynamic range, making quiet sounds quieter. As the sound drops below a certain threshold, the volume is reduced by a greater ratio. This can be very good for covering background noise, or for reducing breath sounds, but must be done carefully, or the drop in volume between loud sounds can sound unnatural.
Gating is like an extreme expander, when sound drops below a certain level it isn’t merely reduced, it’s cut-off. Gating rarely sounds good if left out in the open, and is mostly useful in multitrack applications, or in live-sound to reduce bleed between microphones, automatically turning off a channel that isn’t being actively used. Ambience gets cut-off abruptly, so unless there are enough other sounds to mask this, it can be unpleasant. Try expanding, it’s smoother.
Graphic EQs feature fixed frequency values and fixed bandwidths. Shelving EQs will boost or cut frequencies above or below the defined value. Parametric EQs allow precise adjustments around a center frequency: the amount of boost or cut, and the width of the curve of effected frequencies. That width, or slope, or "Q", is not a constant value, but is a divisor of the center frequency. So a Q value of "3" will create a much wider curve at 12,000hz than it would be at 120hz. Notch filters are parametric EQs with extremely large Q values, and large gain reduction, to precisely eliminate a specific frequency. One must be careful when applying EQ with extremely large Q values, the filters can cause a metallic ringing.
High-Pass filters do just what they say, passing only high frequencies, reducing all signal beneath the defined range, at a defined slope. This filter can be good for reducing rumble and hum, even P-pops. Low-Pass filters do the opposite, reducing frequencies above the threshold frequency, which can be good for reducing hiss, or overly-bright sound. Bandpass filters are combinations of the two previous types, rolling-off sounds above and below a determined frequency range.