What does “this[0]” mean in C#?

Look for an indexer in the class.

C# lets you define indexers to allow this sort of access.

Here is an example from the official guide for “SampleCollection”.

public T this[int i]
    {
        get
        {
            // This indexer is very simple, and just returns or sets 
            // the corresponding element from the internal array. 
            return arr[i];
        }
        set
        {
            arr[i] = value;
        }
    }

Here is the definition from the official language specification:

An indexer is a member that enables objects to be indexed in the same way as an array. An indexer is declared like a property except that the name of the member is this followed by a parameter list written between the delimiters [ and ]. The parameters are available in the accessor(s) of the indexer. Similar to properties, indexers can be read-write, read-only, and write-only, and the accessor(s) of an indexer can be virtual.

One can find the full and complete definition in section 10.9 Indexers of the specification.