What are JavaScript objects and when would they be useful?

Apart from the few primitive types (numbers, strings, booleans, null and undefined) everything is an object in JavaScript (even functions).

Objects are basically containers of properties, which happen to be very useful for collecting and organizing data.

One popular method to create objects is to use the object literal notation:

var emptyObject = {};

var myFirstObject = {
   'name': 'Bobby',
   'surname': 'Smith'
};

The quotes around property names are optional if the name would be a legal JavaScript identifier and not a reserved word. A property's name can be any string. Objects can contain other objects, so they can easily represent trees or graphs:

var myFlight = {
   'airline': 'Airline Name',
   'number': 'AN700',
   'departure': {
      'IATA': 'SYD',
      'time': '2010-09-04 23:10:00'
   },
   'arrival': {
      'IATA': 'LAX',
      'time': '2010-09-05 05:14:00'
   }      
};

JavaScript objects also happen to be a convenient hash table data structure. You could easily do the following:

var myHashTable = {};
myHashTable['name'] = 'Bobby';
myHashTable['surname'] = 'Smith';
alert(myHashTable['name'] + ' ' + myHashTable['surname']);

This is definitely not an exhaustive answer, but I hope it gets you going in the right direction when doing further research.