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Floating-point numbers are a type of numerical data type used in Python to represent real numbers that have decimal points. They are called 'floating-point' because the decimal point can "float"; it can support a large range of values. This is important in programming, especially when dealing with operations that require high precision and when the values are not integers.

In Python, you can create a floating-point number by using the `float()` function. For instance, when you take input from a user that's expected to be a floating-point number, you should convert it to a float using `float(input("Enter a number: "))`.

Floating-point numbers can sometimes behave unpredictably due to the way they are stored in memory. They are stored as approximations, meaning small precision errors can occur. However, they are immensely useful when you need to handle a variety of numbers beyond simple integers.

Conditional statements are the backbone of decision-making in programming. In Python, they are implemented using `if`, `elif`, and `else` statements. These allow the program to execute different code blocks based on certain conditions.

For instance, to find the largest of three numbers, conditional statements are used to continuously compare one number to another and update the largest number based on these comparisons. The logic might look like this:

• Start with assuming the first number is the largest.
• Use an `if` statement to check if the second number is greater than the current ‘largest’. If true, update the largest number.
• Use another `if` statement to compare the third number with the current largest and update as needed.

These steps ensure that the program checks each condition sequentially, updating the largest number when a bigger number is found.

User input is a way for programs to interact with the user. In Python, the `input()` function is used to capture input from the user. It's important to note that input received from `input()` in Python is always treated as a string, so it must be converted to the appropriate data type using functions like `float()` or `int()`.

In the context of the exercise, you ask the user to enter numbers. This input is then stored in variables, and appropriate type conversion is done to treat them as numeric values. Here’s an example:

• `num1 = float(input("Enter the first number: "))`
• `num2 = float(input("Enter the second number: "))`
• `num3 = float(input("Enter the third number: "))`

This ensures that whatever numerical input the user provides is ready for arithmetic operations or comparisons.

Variable comparison is a fundamental operation in programming, allowing the code to evaluate which variables or values meet certain conditions. In Python, comparison operators such as `>`, `<`, `==`, etc., come in handy.

With the exercise at hand, after inputting and storing the floating-point numbers, the next challenge is comparison. You use the `>` operator to continually compare the numbers:

• First, assume the first number is the largest.
• Then, check if the second number is larger using `if num2 > largest:`.
• Again, check if the third number is larger with `if num3 > largest:`.

Each comparison updates the value of a variable that tracks the greatest number found so far, eventually leading to identifying the largest number among the three inputs.