Array
1)Size of array need to be declared in advance.
2)Once declared array can't grow in size.
3)Array can store primitive data types.like int,char,...


Vector
1) No need to declare the size of vector. You may give its size & you may not.
2) Vector can always grow in size if you start adding more element to it than your declared size.
3) Vector can store only object references. Storing primitive data types is not possible in case of vectors.

For starters from Sun;

"An array is a structure that holds multiple values of the same type. The length of an array is established when the array is created. After creation, an array is a fixed-length structure. "

"The Vector class implements a growable array of objects. Like an array, it contains components that can be accessed using an integer index. However, the size of a Vector can grow or shrink as needed to accommodate adding and removing items after the Vector has been created."

For more detail see ;

http://java.sun.com/docs/books/tutorial/java/data/arrays.html

http://java.sun.com/j2se/1.4.2/docs/api/java/util/Vector.html