Beis Shamai says we should light eight candles on the first night, seven on the second night and so on. Beis Hillel says we should light one on the first night, two on the second night and so on. The halacha is like Beis Hillel, so we light one candle on the first night etc.
What is the meaning of their argument?
The light of the Menorah reperesents the light of the Mitzvos which do two things: They push away darkness and add light. Mitzvos Lo saase are the mitzvos that we push away darkness with. Like for example not eating food that isn’t Kosher. Mitzvos Asei are mitzvos that add light because they add good actions to the world, like giving tzedakah.
All Yidden need to do both types of mitzvos. But some yidden focus more on pushing away the bad, like they are extra careful with the food they eat, and some Yidden focus more on mitzvos asei, doing good things.
Now with pushing away the darkness, it requires a lot more strength in the beginning, and then it gets easier as time goes on. With adding light, you start with adding one more good thing, and then you add another and then another.
Beis Shamai were more careful with pushing away darkness, so they felt that the best way to do mitzvos is to light eight candles the first night etc. Which means to be very very strong with being careful not to do the wrong thing, and then putting in less and less energy because it gets easier.
Beis Hillel held of asei tov- adding light, so they held that we should light one candle and then two etc.
The halacha is like Beis Hillel so today, we focus on increasing the mitzvos we do, adding more and more good things to our day, and by doing that we automatically dispel the darkness.