The $_SESSION is a global array in PHP which is always present, if you have called session_start() at the beginning of each file. It is indeed an array and it can store anything you tell it to, like if somebody is logged in:
$_SESSION["isLoggedIn"] = 1;
It makes sense to store some variables in this array, but information like passwordhashes or passwords should NOT be saved in this array. They should in general not be saved anywhere except slated and hashed inside a database.
I do not see what this has to do with forms, but if you have a form there is no need to use this session array. Maybe if the form varies depending on some user specific information. Saving user specific information for each user inside this array is actually what it is supposed to be.
"So I thought, will the forms be built with array " - I do not understand what you mean by this. $_SESSION stores information and does not create forms...
EDIT:
If you want a user to log in and to stay logged in each time he makes a new request to your server (until he logs out or the session expires) you should definitely use the $_SESSION superglobal array. It is said to be pretty secure (if you use it properly of course).