Most modern music is made via software named DAW (Digital Audio Workstation), which is kind of like an IDE but where music is made. These allow you to play with audio (ex: import audio files, arrange them across a timeline, record sound from external sources like a microphone). This is great if you already have all the audio files you need (eg: you're a live band and recorded a song in a studio), but sometimes you want to create new audio without having access to a recording studio.
Audio plugins allow you to create new sounds. You've got two main types of plugins: ones that generate sound (eg: instruments, like a synth) and ones that modify sounds (takes an input sound, modifies it and then outputs it again, like an equalizer/EQ).
Audio plugins are external (or bundled) software that you can use inside a DAW, you can download a lot of them for free but they can also get quite expensive (eg: thousands of dollars). The most popular format for these plugins for a long time (and still today) was VST, but Clap aims to be a new standard to compete with VST.
From the computer's point of view, a host program (probably a DAW) feeds an audio stream to a plugin, eg. 512 samples at a time, the plugin does whatever and sends back 512 samples, which the DAW may optionally route to another plugin and so on. Plugins are routed by software, instead of the 1/4" jack cables used by most hardware effects pedals.
Modern audio production often uses a lot of these effects / plugins, like dozens or hundreds across a multi-track project, then a bunch more once the tracks are mixed together. Each plugin can either affect the sound very subtly, or make it completely unrecognizable, or something in the middle.
Contains some omissions and half-truths, but that's kind of the gist of it.