Vector is a legacy collection class from Java 1.0. In Java 1.2 (long ago!), the Collections Framework was added which included new collection classes such as ArrayList and HashMap, which were intended to replace the legacy classes Vector and Hashtable.
As said before, the legacy collection classes had built-in synchronization, which is unnecessary for many applications. Synchronization has a performance overhead, so if it's not necessary, you shouldn't use it.
In some cases (when your program is multi-threaded, and multiple threads access the same data) you need to synchronize your collections. Some people would then use the old Vector or Hashtable classes, but a better way is to use a synchronization wrapper with for example an ArrayList:
// Your standard, unsynchronized list
List<String> data = new ArrayList<String>();
// Use this to put it into a synchronization wrapper
List<String> syncedData = Collections.synchronizedList(data);
See the API documentation of Collections.synchronizedList() (and other methods) for more information.