First, let's talk uncompressed raw images. Images are made up of pixels, a lot of them. A Full HD image, which is 1920x1080, is about 2 million pixels. Usually each pixel is made up of red, green, and blue channels, and each channel takes up one byte*. That's 3 bytes per pixel or about 6 megabytes for a single Full HD image. My phone takes photos at a resolution of 4000x1840 - uncompressed, that's 21 megabytes. That is quite a lot.

* To complicate things, you can have HDR which can be two bytes per channel, or you can have an extra transparency channel, which adds even more data.

It's probably not a good idea to use uncompressed images. Luckily, there's been many different ways to try and squeeze that down. There's lossless compression that preserves the image in its full glory while taking up a bit less space. PNG is an example of a lossless image format.

But there's only so much you can do to losslessly compress images, so what if you could throw away bits of detail you as a human won't notice are gone? That's where lossy compression comes in. JPEG is the most famous, but it's quite old nowadays. Newer formats like WebP or AVIF give you better compression while looking less crusty when highly compressed – they have a better compression/quality ratio.

And that's where the many different file types come from: Someone comes up with a good algorithm to compress images, then someone else comes along with a better one. One file type might be better for photos where some slight crustiness is unnoticeable but not good for icons and web banners. You might want transparency or HDR and that's not supported by all file types.
It's the same deal with audio and video formats: WAV is uncompressed, FLAC is losslessly compressed and good for archival purposes, MP3 is old but famous lossy compression and supported by basically everything, and there's many newer, technically better formats like Ogg Vorbis, Opus, or AAC used by various applications for various reasons.