const means it can never be changed after it is first created
const is short for constant and one of its uses is to define, well, constants. In the code above, wordList is an array of string constants. This means that, after they are initialized, you can't change their values.
std::strings like the ones in the code above are C++ style strings. A C style string, commonly called a C-string, is a sequence of characters terminated by the null character ('\0'). Unless you really have to, it's not a good idea to work with C-strings, as std::strings are easier to use.
EDIT: Unless you're talking about microsoft's CString, which is a class (user defined type) similar to std::string.