1. Your fish produces ammonia from the food they eat.
2. Microorganisms convert the ammonia (NH3) to nitrite (NO2)
3. Different microorganisms turn nitrite to nitrate (NO3)

Microorganisms in your filter, mostly archaea in fresh water filters, will turn the ammonia produced by your fish into nitrite and then other microorganisms will turn this into Nitrates.

Ammonia and Nitrites are both very toxic and your test kit should read 0, if it doesn’t you need to do a water change and get the readings down to 0.

Nitrates are less toxic, and in an ideal world need to be below 15 ppm. Be aware most test kits need shaking to hell to work properly. Your tap water however may have higher levels.