Q: Arrays vs Vectors: Introductory Similarities and Differences What are the differences between an array and a vector in C++? An example of the differences might be included libraries, symbolism, abilities, etc.
Array

Arrays contain a specific number of elements of a particular type. So that the compiler can reserve the required amount of space when the program is compiled, you must specify the type and number of elements that the array will contain when it is defined. The compiler must be able to determine this value when the program is compiled. Once an array has been defined, you use the identifier for the array along with an index to access specific elements of the array. [...] arrays are zero-indexed; that is, the first element is at index 0. This indexing scheme is indicative of the close relationship in C++ between pointers and arrays and the rules that the language defines for pointer arithmetic.
— C++ Pocket Reference

Vector

A vector is a dynamically-sized sequence of objects that provides array-style operator[] random access. The member function push_back copies its arguments via copy constructor, adds that copy as the last item in the vector and increments its size by one. pop_back does the exact opposite, by removing the last element. Inserting or deleting items from the end of a vector takes amortized constant time, and inserting or deleting from any other location takes linear time. These are the basics of vectors. There is a lot more to them. In most cases, a vector should be your first choice over a C-style array. First of all, they are dynamically sized, which means they can grow as needed. You don't have to do all sorts of research to figure out an optimal static size, as in the case of C arrays; a vector grows as needed, and it can be resized larger or smaller manually if you need to. Second, vectors offer bounds checking with the at member function (but not with operator[]), so that you can do something if you reference a nonexistent index instead of simply watching your program crash or worse, continuing execution with corrupt data.
— C++ Cookbook


A: I'll add that arrays are very low-level constructs in C++ and you should try to stay away from them as much as possible when "learning the ropes" -- even Bjarne Stroustrup recommends this (he's the designer of C++).  
Vectors come very close to the same performance as arrays, but with a great many conveniences and safety features. You'll probably start using arrays when interfacing with API's that deal with raw arrays, or when building your own collections.

A: arrays:

*

*are a builtin language construct;

*come almost unmodified from C89;

*provide just a contiguous, indexable sequence of elements; no bells and whistles;

*are of fixed size; you can't resize an array in C++ (unless it's an array of POD and it's allocated with malloc);

*their size must be a compile-time constant unless they are allocated dynamically;

*they take their storage space depending from the scope where you declare them;

*if dynamically allocated, you must explicitly deallocate them;

*if they are dynamically allocated, you just get a pointer, and you can't determine their size; otherwise, you can use sizeof (hence the common idiom sizeof(arr)/sizeof(*arr), that however fails silently when used inadvertently on a pointer);

*automatically decay to a pointers in most situations; in particular, this happens when passing them to a function, which usually requires passing a separate parameter for their size;

*can't be returned from a function; (Unless it is std::array)

*can't be copied/assigned directly;

*dynamical arrays of objects require a default constructor, since all their elements must be constructed first;

std::vector:

*

*is a template class;

*is a C++ only construct;

*is implemented as a dynamic array;

*grows and shrinks dynamically;

*automatically manage their memory, which is freed on destruction;

*can be passed to/returned from functions (by value);

*can be copied/assigned (this performs a deep copy of all the stored elements);

*doesn't decay to pointers, but you can explicitly get a pointer to their data (&vec[0] is guaranteed to work as expected);

*always brings along with the internal dynamic array its size (how many elements are currently stored) and capacity (how many elements can be stored in the currently allocated block);

*the internal dynamic array is not allocated inside the object itself (which just contains a few "bookkeeping" fields), but is allocated dynamically by the allocator specified in the relevant template parameter; the default one gets the memory from the freestore (the so-called heap), independently from how where the actual object is allocated;

*for this reason, they may be less efficient than "regular" arrays for small, short-lived, local arrays;

*when reallocating, the objects are copied (moved, in C++11);

*does not require a default constructor for the objects being stored;

*is better integrated with the rest of the so-called STL (it provides the begin()/end() methods, the usual STL typedefs, ...)

Also consider the "modern alternative" to arrays - std::array; I already described in another answer the difference between std::vector and std::array, you may want to have a look at it.

A: Those reference pretty much answered your question. Simply put, vectors' lengths are dynamic while arrays have a fixed size.
when using an array, you specify its size upon declaration:
int myArray[100];
myArray[0]=1;
myArray[1]=2;
myArray[2]=3;

for vectors, you just declare it and add elements
vector<int> myVector;
myVector.push_back(1);
myVector.push_back(2);
myVector.push_back(3);
...

at times you wont know the number of elements needed so a vector would be ideal for such a situation.
