Recurrence relations are really important for understanding how well divide-and-conquer algorithms work. They help us look at the time it takes to solve problems.

Here’s how they work:

1. Breaking Down Problems: Recurrence relations show us how a big problem can be split into smaller problems. For instance, in merge sort, we can say that the time to solve the problem ($T(n)$) is made up of solving two smaller problems ($2T(n/2)$) and doing some extra work ($O(n)$).

2. Analyzing Efficiency: We can use something called the Master Theorem to look at equations like $T(n)$. This helps us figure out the time complexity right away. Through this, we can learn about how well an algorithm performs and how we can make it better.

In short, recurrence relations are a helpful way to check how efficient algorithms are in a clear and organized manner.