'When I walked in the park [in Hong Kong], I thought: 'Oh my goodness, this is where I walked with Walt Disney',' Mr Sklar said.
In British usage, we call ( ) brackets or round brackets, and [ ] square brackets.
(The Americans call ( ) parentheses and [ ] brackets.)
The word, phrase or sentence within the round and square brackets is called a parenthesis. We use round and square brackets when we wish to provide extra information or an explanation. The difference is that square brackets are used when the sentence is a quotation: either from a printed source (e.g. books, newspapers) or a person's words.
In the above example, square brackets are used because the sentence is Mr Sklar's words. The phrase 'in Hong Kong' is added to let readers know that the park he was referring to is in Hong Kong, not in Paris or Tokyo.
The test of a parenthesis is that when it is taken out, the sentence still makes sense and still flows. (See 'e.g. newspapers, books' and 'The Americans ... brackets'.)