Well temperament is a way of tuning musical notes so they sound good together. It's like when you're singing with your friends, if you are all singing different pitches or notes, it might sound a bit off or not as nice as when you are all singing the same notes.
In traditional tuning, notes are usually divided into 12 equal parts, called semitones. But in well temperament, the distance between notes is slightly different depending on where they are in the scale. This means that each note has a different "colour" or "feeling" to it, and that some notes might sound better than others when played together.
It's like when you are trying to colour in a picture with your crayons, and sometimes the colours you use don't match perfectly, but you try to make them look good together anyway.
Well temperament was created a long time ago, before the piano was invented, and it was used mostly for string instruments like the violin. But now, many musicians use well temperament on instruments like the piano, because it allows them to play music that sounds really beautiful and expressive.