please explain the logic of ExtentReports rep = ExtentManager.getinstance();

public static ExtentReports getInstance() {

this is the confuding line. 

usually we write

public static object[] sun(){

how a class can be a return type?

This class is supposed to return you ExtentReports Object reference

A function can also return object reference

For example when we write

WebElement e = driver.findElement(By...);

Here Find Element function returns reference of WebElement .

in this case, if webEliment class has methods a(), b(),  and c().  and findElement() has methods x(), y() and z(). by writing WebElement e = driver.findElement(By...); which all methods can be called using the reference e?

e can access

a,b,c