A hash function is a fundamental concept in data structures and plays a crucial role in various applications, such as hash tables and data retrieval. It is a mathematical function that takes an input (or "key") and produces a fixed-size output, often a numerical value or a string of characters. The primary purpose of a hash function is to map data of arbitrary size to a fixed-size hash code. Here, I will discuss the properties of hash functions in the context of data structures.

**1. Deterministic:** A hash function must be deterministic, meaning that for a given input, it will always produce the same output. This property ensures consistency in hash code generation and retrieval.

**2. Fast Computation:** Hash functions should be computationally efficient to calculate the hash code, as they are often used in time-critical applications like searching and data retrieval.

**3. Uniform Distribution:** A good hash function should distribute keys uniformly across the range of possible hash codes. In other words, it should minimize collisions, where multiple keys map to the same hash code. This property helps maintain the efficiency of data structures like hash tables.

**4. Pre-image Resistance:** It should be computationally infeasible to reverse the hash code to determine the original input key. This property ensures the security of hash functions in applications like password hashing.

**5. Avalanche Effect:** A minor change in the input should result in a significantly different hash code. This property ensures that small variations in data lead to completely different hash codes, preventing clustering of similar keys in the data structure.

**6. Fixed Output Size:** A hash function should always produce hash codes of a fixed size, regardless of the input key's size. This property is essential for consistent storage in data structures like hash tables.

**7. Efficient to Compute:** Hash functions should be designed to be computationally efficient, ensuring that the hashing process doesn't become a bottleneck in the overall performance of data structures.

**8. Low Collision Probability:** While no hash function can entirely eliminate collisions, a good hash function should strive to keep the probability of collisions low, minimizing the need for additional collision resolution techniques.