I assume that you mean curly braces when you say brackets...
Curly braces enclose units of code. For example if you write:
class something {}
those curly braces mean that everything between them is a part of this class.
I'm also going to assume that you mean semicolons ( ; )
Semicolons mark the end of a java statement. For example:
double someNumber;
means that you're creating a variable called someNumber, and that it's of the type Double. You have nothing more to say about someNumber so you end the statement with a semicolon.
EDIT: if you actually meant brackets, then I can tell you that brackets are used with arrays. To be more specific they enclose the indexing expressions of an array. For example:
int[] someArray;someArray = new int[3];
the first line declares an (empty) array of integers, the second line initializes the array with 3 int values.