Lambda expressions allow functions to be used as variables or fields through special syntax using the => operator, which separates the function parameters and body. The document provides examples of lambda expressions with different parameter types and bodies. It also explains that the => operator separates the left side (parameters) from the right side (body) and is not a comparison operator in this context. LINQ (Language Integrated Query) introduces extension methods that allow querying collections like lists and arrays, even those not yet in memory. An example uses the Average extension method to calculate the average of all elements in an integer array.