Why bother? Because your stock Android phone probably comes with a sh1tload of applications you don’t need and is infested with Google spy tools. Many custom roms build on top of AOSP (Android Open Source Project) and tailor it for your phone’s hardware. My favorite project is LineageOS, the successor of the now defunct CyanogenMod. But to be honest, I haven’t tried much else.
AOSP roms come without any Google applications (short: GApps) to begin with. But since life without Play Store and Play Services is going to be difficult, you’re going to want to have a minimum set of GApps. To get those, right after flashing your custom rom*, flash a GApp package. There are different packages out there, NikGapps, MindTheGapp, OpenGapps. I highly recommend going with OpenGapps because it allows you to restore your Google Backup! Also note that.
* If you accidentally reboot into system after flashing the custom rom, do a factory reset (only resets the new OS), then go directly back into TWRP and flash your GApps package.