Think we wanna analyise a flower and try to make sense of how it changes. In the traditional view, we would look at the flower in any particular instance and be able to make statements about it's make up right then and there. Like first it is just a seed, than we get a stage where leaves grow, later buds and even later the actual flower.
But in an dialectical view, it's all part of the same process of becoming, you can not make sense of the flower without containing the earlier stages in the same thought. Furthermore, while in the traditional sense, the bud and the flower conradict each other (everytime youu look at it only one can exist, if the plant has buds it can not yet flower, if it flowers the bud is gone), while in the dialectical sense they even necessitate each other, you can't have the flower without having the bud or the seed first. Both bud and seed are parts of the flowers being at any time and have to be kept in mind.
The same is true for when we analyse the becoming of societies. In the traditional view, enlightenment, the nazi regime and modern liberal democracy are seperate and even exclusionary steps in the history of the german nation. But through the lense of dialectics, they are part of the same movement and are dependent on each other. It allowes us to delve deeper in the mechanisms that made one become the other stage and thus gives us a much more complete understanding.
I'm sorry if I poorly worded things, I only know the german terms for alot of stuff here, but I hope you get the gist.