Create a Python function that takes a list of integers as input andreturns a new list containing only the prime numbers from the input list.Provide a clear explanation of your implementation and include a test case.

Sure, here is a Python function that filters out the prime numbers from a given list of integers.

def filter_primes(num_list):
    def is_prime(n):
        if n < 2:
            return False
        for i in range(2, int(n**0.5) + 1):
            if n % i == 0:
                return False
        return True

    primes = [num for num in num_list if is_prime(num)]
    return primes

Explanation:

1. The function filter_primes takes a list of integers as input.
2. Inside this function, we define another function is_prime that checks if a given number is prime.
3. is_prime function works by checking if the number is less than 2 (the smallest prime number) and returns False if it is.
4. If the number is 2 or greater, it checks if the number can be divided evenly by any number from 2 to the square root of the number. If it can, it returns False (meaning the number is not prime).
5. If the number cannot be divided evenly by any other number (other than 1 and itself), it returns True (meaning the number is prime).
6. We then use a list comprehension to create a new list that contains only the numbers from the input list that are prime. This is done by checking each number with the is_prime function.
7. Finally, the function returns the list of prime numbers.

Test case:

print(filter_primes([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]))

This should output: [2, 3, 5, 7]