Difference between abstraction and encapsulation?

Most answers here focus on OOP but encapsulation begins much earlier:

• Every function is an encapsulation; in pseudocode:

  point x = { 1, 4 }
  point y = { 23, 42 }
  
  numeric d = distance(x, y)
  

  Here, distance encapsulates the calculation of the (Euclidean) distance between two points in a plane: it hides implementation details. This is encapsulation, pure and simple.

• Abstraction is the process of generalisation: taking a concrete implementation and making it applicable to different, albeit somewhat related, types of data. The classical example of abstraction is C’s qsort function to sort data:

  The thing about qsort is that it doesn't care about the data it sorts — in fact, it doesn’t know what data it sorts. Rather, its input type is a typeless pointer (void*) which is just C’s way of saying “I don't care about the type of data” (this is also called type erasure). The important point is that the implementation of qsort always stays the same, regardless of data type. The only thing that has to change is the compare function, which differs from data type to data type. qsort therefore expects the user to provide said compare function as a function argument.

Encapsulation and abstraction go hand in hand so much so that you could make the point that they are truly inseparable. For practical purposes, this is probably true; that said, here’s an encapsulation that’s not much of an abstraction:

class point {
    numeric x
    numeric y
}

We encapsulate the point’s coordinate, but we don’t materially abstract them away, beyond grouping them logically.

And here’s an example of abstraction that’s not encapsulation:

T pi<T> = 3.1415926535

This is a generic variable pi with a given value (π), and the declaration doesn’t care about the exact type of the variable. Admittedly, I’d be hard-pressed to find something like this in real code: abstraction virtually always uses encapsulation. However, the above does actually exist in C++(14), via variable templates (= generic templates for variables); with a slightly more complex syntax, e.g.:

template <typename T> constexpr T pi = T{3.1415926535};

Many answers and their examples are misleading.

Encapsulation is the packing of "data" and "functions operating on that data" into a single component and restricting the access to some of the object's components.
Encapsulation means that the internal representation of an object is generally hidden from view outside of the object's definition.

Abstraction is a mechanism which represent the essential features without including implementation details.

Encapsulation:-- Information hiding.
Abstraction:-- Implementation hiding.

Example (in C++):

class foo{
    private:
        int a, b;
    public:
        foo(int x=0, int y=0): a(x), b(y) {}

        int add(){    
            return a+b;   
        } 
}  

Internal representation of any object of foo class is hidden outside the class. --> Encapsulation.
Any accessible member (data/function) of an object of foo is restricted and can only be accessed by that object only.

foo foo_obj(3, 4);
int sum = foo_obj.add();

Implementation of method add is hidden. --> Abstraction.

Encapsulation is hiding the implementation details which may or may not be for generic or specialized behavior(s).

Abstraction is providing a generalization (say, over a set of behaviors).

Here's a good read: Abstraction, Encapsulation, and Information Hiding by Edward V. Berard of the Object Agency.

encapsulation puts some things in a box and gives you a peephole; this keeps you from mucking with the gears.

abstraction flat-out ignores the details that don't matter, like whether the things have gears, ratchets, flywheels, or nuclear cores; they just "go"

examples of encapsulation:

• underpants
• toolbox
• wallet
• handbag
• capsule
• frozen carbonite
• a box, with or without a button on it
• a burrito (technically, the tortilla around the burrito)

examples of abstraction:

• "groups of things" is an abstraction (which we call aggregation)
• "things that contains other things" is an abstraction (which we call composition)
• "container" is another kind of "things that contain other things" abstraction; note that all of the encapsulation examples are kinds of containers, but not all containers exhibit/provide encapsulation. A basket, for example, is a container that does not encapsulate its contents.