LFO stands for Low Frequency Oscillation. An LFO is a signal below 20Hertz that is used to modulate another signal. In synthesis it is used to make a wub, wub sound or it can be used to create a verity of filter effects.
I'll describe it in layman’s terms first and then in more technical detail.
An LFO is a very, very, very slow waveform/signal. It is so slow you cannot hear what is being played. This makes it a great option for very slowly modulating parameters such as volume, filters, cut offs, pitch, and other things.
To understand how an LFO works you must first understand signal flow. This varies in digital and analogue signal. I'm going to stick to digital. In digital synthesis you have information being passed around that tells your synthesizer how to play a sound. In essence it is binary. This binary, or code, is being processed in an order called "routing". For example, you may tell your sound to generate by hitting a key, then pass through a filter, and then a chorus effect, OR you can tell it to go through the chorus effects and then the filter! Each one will produce unique results. The best synthesis engines allow you to control this, however not all synths do.
It is important to note that there are two kinds of signals in this process; one signal is your sound, and the other signal is the effects, telling your sound what to do. For example, we have a sound that is being routed into the chorus effect. Your sound is a signal, and the chorus effect is changing that signal, BUT your chorus effect is taking another signal in. This other signal tells the chorus effect how to affect your sound! This signal is not an audio signal in the sense that we are going to hear it, rather it is a controlling signal that carries code to tell your synth what to do. There is where the LFO comes in.
In this code carrying signal path you tell your program to introduce a much slower waveform that we call an LFO. When you do this you are generally (it can get pretty crazy) telling a parameter of that effect to turn all the way off and on as the wave form peaks to its highest value and reaches its lowest value. In this way you can accomplish an insane amount of variation in a sound, you may even go so far as to limit how far the LFO can move and even set up subset LFO's that are controlling parameters that are controller your original LFO! If you understood all that then good for you, if you didn't then don't worry! It will come as you gain experience and the magic of LFO's will come to you. To help you learn these processes please do the two examples below.
Another quick important note is that you can change the speed of the LFO by changing the frequency of it, thus letting you change how quickly it turns a parameter on and off! Great for live performance!
Here are some basic ways on how I would use and LFO. I'll give two examples:
1. Lets say I have a sound that I want to turn into a wub wub sound. I can do this a verity of ways, but I would like to use an LFO as this can let me very the speed of the wub easily. So I find my LFO signal generator (this is synth specific so you may need to read the Manuel a bit to see how they have set up the routing in your particular synth), and link it to my volume. Boom! Now my bass is wobbling! I can change the speed of the wobble by changing the pitch of the LFO (This is commonly labeled as "amount" in a synth").
2. Now let’s say I would just like some variation in the synth by a filter, but you want the filter parameters to move on their own. This can be done using an LFO! All you must do is the exact same thing you did in exercise 1 but with the parameter you want to move! It should be noted that not all parameters in synth engines let you have access to linking an LFO to them. So if you don't see a way to link it, it may not be there. Read the manual to find out.
Some synths let you do this all over the place and some do not. Those famous for presets such as Nexus do not give you very much control over your sound with in the module. You may be able to overcome this limitation with 3rd party plug-ins, but instead of that route you may decide to just use a more powerful synth engine. "Massive" is built around this concept and is an awesome tool for this reason. Serum, Harmor, and Sytrus also are great tools in the respect.