String text = \'[[\"item1\",\"item2\",\"item3\"], [\"some\", \"item\"], [\"far\", \"out\", \"string\"]]\';
I would like to iterate over each individual
This syntax looks like a subset of JSON, and I would guess that the client side is actually encoding it as JSON. Assuming that is true, the simplest approach will be to use an off-the-shelf JSON parser, and some simple Java code to convert the resulting objects into the form that your code requires.
Sure, you could implement your own parser by hand, but it is probably not worth the effort, especially if you have to deal with string escaping, possible variability in whitespaces and so on. Don't forget that if you implement your own parser, you NEED TO IMPLEMENT UNIT TESTS to make sure that it works across the full range of expected valid input, and for invalid input as well. (Testing the cases of invalid input is important because you don't want your server to fall over if some hacker sends requests containing bad input.)
Before you go any further, you really need to confirm the exact syntax that the client is sending you. Just looking at an example is not going to answer that. You either need a document specifying what the syntax is, or you need to look at the client / application source code.