This week's book giveaways are in the iOS and Features new in Java 8 forums. We're giving away four copies each of Barcodes with iOS: Bringing together the digital and physical worlds and Core Java for the Impatient and have the authors on-line! See this thread and this one for details.
You can view a vector as a "growable" array. That is, the vector grows or shrinks according to how many items your add or remove to or from it. The major difference is that you can only store objects (or object references) in a vector. An array can store primitive data types in addition to object references.
Having said that, you would be well advised to use the ArrayList class in place of a vector. The ArrayList is part of the Java Collections framework and is more efficient. Anything you can do with a vector, you can do with an ArrayList. The difference between the two collections is that Vector is synchronised whereas ArrayList (plus any of the other new collection implementations_ is not. From a beginner's learning point of view, this is not an issue. You can learn more about this when you learn about threads.
As suggested in a previous reply, check out the API documentation for these classes to learn more.