What does it mean and || p () (0); in Javascript?

Although amenadiel gave a good answer, I want to give another reference and explaining what the operator refers to || when you work with variables like in the example you showed

function test(argument){
  // Si el argumento no es dado se pondrá por defecto 'Hello world'
  argument = argument || 'Hello world';
  return argument;
}

console.log(test('Hola mundo')); // Hola mundo
console.log(test());             // Hello world

Then in your case

// Esto equivaldría a que si y no está definida y/o inicializada su valor dependerá de lo que retorne la función p()(0)
y || p()(0);

Example of the above:

function test(argument){
  argument = argument || override('Hello world')
  return argument;
}

function override(data){
  return test(data);
}

console.log(test('Hola mundo')); // Hola mundo
console.log(test('Hey!'));       // Hey! 
console.log(test());             // Hello world

p is a function that returns another function f

p()(0) 

Equivalent to do

f(0)

That said, the expression

y || f(0)

Evaluate true if y or f(0) are "true" ( truthy ).

With a minified code, it is no longer what can be said.