what is the difference between declarative and imperative programming

A great C# example of declarative vs. imperative programming is LINQ.

With imperative programming, you tell the compiler what you want to happen, step by step.

For example, let's start with this collection, and choose the odd numbers:

List<int> collection = new List<int> { 1, 2, 3, 4, 5 };

With imperative programming, we'd step through this, and decide what we want:

List<int> results = new List<int>();
foreach(var num in collection)
{
    if (num % 2 != 0)
          results.Add(num);
}

Here, we're saying:

1. Create a result collection
2. Step through each number in the collection
3. Check the number, if it's odd, add it to the results

With declarative programming, on the other hand, you write code that describes what you want, but not necessarily how to get it (declare your desired results, but not the step-by-step):

var results = collection.Where( num => num % 2 != 0);

Here, we're saying "Give us everything where it's odd", not "Step through the collection. Check this item, if it's odd, add it to a result collection."

In many cases, code will be a mixture of both designs, too, so it's not always black-and-white.

C# is a much more imperative programming language, but certain C# features are more declarative, like Linq

dynamic foo = from c in someCollection
           let x = someValue * 2
           where c.SomeProperty < x
           select new {c.SomeProperty, c.OtherProperty};

The same thing could be written imperatively:

dynamic foo = SomeCollection.Where
     (
          c => c.SomeProperty < (SomeValue * 2)
     )
     .Select
     (
          c => new {c.SomeProperty, c.OtherProperty}
     )