What is the meaning of "this [int index]"?

That is an indexer defined on the interface. It means you can get and set the value of list[index] for any IList<T> list and int index.

Documentation: Indexers in Interfaces (C# Programming Guide)

Consider the IReadOnlyList<T> interface:

public interface IReadOnlyList<out T> : IReadOnlyCollection<T>, 
    IEnumerable<T>, IEnumerable
{
    int Count { get; }
    T this[int index] { get; }
}

And an example implementation of that interface:

public class Range : IReadOnlyList<int>
{
    public int Start { get; private set; }
    public int Count { get; private set; }
    public int this[int index]
    {
        get
        {
            if (index < 0 || index >= Count)
            {
                throw new IndexOutOfBoundsException("index");
            }
            return Start + index;
        }
    }
    public Range(int start, int count)
    {
        this.Start = start;
        this.Count = count;
    }
    public IEnumerable<int> GetEnumerator()
    {
        return Enumerable.Range(Start, Count);
    }
    ...
}

Now you could write code like this:

IReadOnlyList<int> list = new Range(5, 3);
int value = list[1]; // value = 6

That is an indexer. So you can access the instance like an array;

See MSDN documentation.