A method has 5 parts, three of which are optional.
[flags] ReturnType name([ParameterList]) { [code] }
The [flags] is an optional part of a method that indicates what kind of method it is. Many very important indications of what a method can do and how it can be used go here. When present [flags] is a list of words such as public, private, protected, static, final, and synchronized. When a method is private that means it can only be used from inside the same class. When a method is static, that means that it can be used without an instance of the class. Your main method is static so it doesn't have an instance of its class, so unless you find an instance somewhere you will only be able to call static methods of that class.
So a private static method is good for you because main is in the same class and you can use a static method without creating an object first.
The ReturnType says what sort of value the method produces as a result. In this case you want a true or false to indicate whether the string is a binary number containing only 1s and 0s. Methods that return true or false have boolean as the return type. ReturnType is not optional; even methods that produce no result have void in the ReturnType place.
name is what you want to call your method and how you will use your method. It can be almost anything except for a few reserved words, but by convention it starts with a lower-case letter, like isBinary. Putting isBinary as the name means that you would use your method like this: isBinary(input). Using a method is called calling the method, and when a method is called it is replaced by the result that it produces. So when your application is running if(isBinary(input)) would become if(true) or if(false) depending on whether input is a binary number or not, so using this method makes it very easy to write your application.
The [ParameterList] part is optional and surrounded by (). It represents the values that your method needs to work with to decide on the result that it will produce. In this case, you want something like String value which means that isBinary needs a string and it will be named value in the code of the method. Even if you have no [ParameterList] you would still need the ().
The [code] part is where you say what you want your method to do. The [code] part is optional; some methods do nothing, but only when ReturnType is void, because otherwise your method needs to at least produce a result. In your case you want [code] to check input for being a binary number and then use a return statement to produce a result that is either true or false.
So now I hope the meaning of private static boolean isBinary(String value) is clear.