It's just an array declaration. That means stringname
holds an array of strings (or rather, it declares an array-of-strings variable, since it doesn't actually hold anything yet).
There are a few variations in C# for declaring arrays and initializing. There's a good rundown here.
var arr1 = new string[5]; // empty array of length 5
string[] arr2 = { "a", "b", "c" }; // pre-populated array with 3 items