Modulating the pitch of a sound with a sine wave LFO produces a sound that goes up and down cyclically (following the ups and downs of the sine wave) from the base pitch (of that sound without modulation). This modulation of the pitch is referred to as VIBRATO. If you modulate the amplitude (loudness) or the filter cutoff of the sound instead of the pitch, the effect is often called TREMOLO. When the LFO is a square or rectangle wave modulating the pitch, you obtain an effect called TRILL (goes back and fourth between 2 pitch values).
What is a sample-and-hold (S-H) wave? It is a stepped signal coming from a source signal (usually some random noise coming from an internal noise generator) sampled by a clock source. When the clock sends its trigger to the LFO module, it samples its source signal and holds the sampled value until the next trigger. In other words, the source signal is sampled at regular intervals forming a stepped signal, each step corresponding to the value of a sample.
It is called Low-Frequency because it operates usually under the 20 Hz threshold (of things that you can't really hear by themselves).
Above is what you see when you go into SYNTH PATCH for synth1 or synth2. In this post, we focus on the MG (Modulation Generator) module.
As you can see, KORG calls an LFO a Modulation Generator (MG), which is not a bad name since it's exactly that. The supported waveforms are: triangle, sawtooth, pulse (square) and sample-and-hold. The output wave of the Modulation Generator can serve as input to whatever module accepts modulation. The frequency knob controls the frequency of the signal, in other words, its speed. The BPM (Beat-Per-Minute) slider switch enables you to force the LFO's frequency to be in sync with the main beat (per minute).
The two jacks on the right of the MG panel (as seen above) are for modulation with the Envelope Generator (EG) and the second oscillator (VCO2). Those two have nothing to do with the Low-Frequency Oscillator (LFO), they are just other sources of modulation.
So, to be perfectly precise, KORG's MG (Modulation Generator) is not exactly equivalent to an LFO (Low-Frequency Oscillator) as it includes the LFO and other sources of modulation (EG and VCO2 on the Nintendo DS version of the KORG MS-10).