Alright kiddo, imagine you're playing a game and your friend has a turn before you. When it's your turn, you have to do something even better than what your friend did. This is kind of like the idea of the "successor ideology."
In grown-up terms, it's a way of thinking that says we always have to do better than the people who came before us. This means we have to work really hard to fix problems that haven't been solved yet, even if it's really tough.
One example of this is when people talk about how our world needs to be more fair and equal for everyone. Some people might say that things have gotten better for some groups over time, but there's still a lot of work to be done.
The idea of the successor ideology says that we can't just stop working to make things better because some progress has been made. Instead, we have to keep going and make even more progress so that everybody can have a fair chance.