A VST is essentially a small program that gets loaded into your Digital Audio Workstation (a larger program). VSTs are generally of two types, Synths/Instruments or Effects. Effect VSTs take an input signal (your original sound) and output a modified signal after the effect is applied. Synths generate waveforms (the sound) through mathematical algorithms tailored to achieve a specific sound the author wanted to get. Instrument VSTs are generally sample based, albeit sometimes extremely complicated. Some grand piano instruments can take up 12-16 gigs of pure uncompressed samples (just for one instrument!).
Some good effects VSTs to get started on are bootsy's collection at variety of sound
Some good synths to try out are the Korg legacy collection synths, especially the M1 and WAVESTATION (my two favorites)
other synth brands to check out are G-Force and tone2
sorry I can't post links to them but I don't have a high enough post count.