My update doesn't work

You would have to pass a user ID per session ... so that the update of your WHERE is governed there (where your little problem is)

In the code you passed, there is no "$email" variable, but "$emai"

WHERE email='$email'

(---Approach---) If I have all my data and as email "[email protected]" I want to change it to "[email protected]" in your WHERE it will look for the email [email protected] to change it by [email protected] and it will not look for [email protected] (depending on the query you are using, unless you save its current email as session or pass it through input hidden (which is later implemented in a few more lines to control that they do not manipulate it before sending it to php+sql))

<?php

    session_start();
    require conexion.php;

    extract($_POST); // importa a la lista de variables lo que llega por $_POST

    // Create connection
    $conn = new mysqli($servername, $username, $password, $dbname);

    // Check connection
    if ($conn->connect_error) {
        die("Oops: " . $conn->connect_error);
    }

    if (isset($_SESSION['usuario'])) {

        $cambio = "UPDATE Usuarios SET name='$nombre', email='$emai', password='$pass', phone='$tel', address='$dir' WHERE ID='$id'";        

        if (($conn->query($cambio))) 
        {
            echo $_SESSION['usuario']['name'];
        } else {
            echo "Error: ";
        }

    } else {

        echo"oops";

    }

    $conn->close();

?>

However, since I can't see the connection.php file, it's impossible to find out if the connection is right...

I hope I helped you.

Cheers

Another error apart from those that have been modified by the comments is in the following step:

if (($result=$conn->query($cambio)) === true) {

I see too many open and close braces (), in fact I did a test, and it sends me an error.

error: Fatal error: Call to a member function query() on null in... , liking on that line.

You could do something like this:

$result = $conn->query("UPDATE Usuarios SET name='$nombre', email='$emai', password='$pass', phone='$tel', address='$dir' WHERE ID=$id"); 

if (true===$result) { }

either

if ($conn->query($cambio) === true)      

A possible example:

connection.php

$conn = new mysqli("servidor", "usuario", "contraseña", "BaseDatos");

/* verificar conexión */
if (mysqli_connect_errno()) {
    printf("Conexión fallo: %s\n", mysqli_connect_error());
    exit();
} else {
    //echo 'Existe conexión.';
}

UPDATE

<?php
    session_start();        
    //Reset
    $nombre = $emai = $pass = $tel = $dir = $id = NULL;

    //Si esta definido el formulario
    if (isset($_POST['sumbitt'])) {     
        //Obtener datos del formulario
        $nombre = $_POST['nombre'];
        $emai   = $_POST['emai'];
        $pass   = $_POST['pass'];
        $tel    = $_POST['tel'];
        $dir    = $_POST['dir'];
        $id     = $_SESSION['usuario']['ID'];

        //Si esta definido la sesion.
        if (isset($_SESSION['usuario'])) {
            //Verdadero datos a trabajar.
            if ($nombre && $emai && $pass && $tel && $dir && $id) {
                //Conexion (Importante llamar a la conexión dodne vas a trabajar con el).
                require 'conexion.php';
                //Sentencia
                $result = $conn->query("UPDATE Usuarios SET name='$nombre', email='$emai', password='$pass', phone='$tel', address='$dir' WHERE ID=$id");        
                //Comprabación si se ejecuto la sentencia.
                if (true===$result) {
                    echo $_SESSION['usuario']['name'];
                } else {
                    exit('Fallo el update: ' . htmlspecialchars($conn->error));
                }                   
            }
        } else {
            echo"oops hubo un error en tu sesión.";
        }   
    }

?>

Note: I advise you for security to use mysqli prepare or PDO statements. I also advise you to read well How to avoid SQL injection in PHP?

I suggest you try this solution. In her:

1. I apply the principle of prepared queries to give security to the code
2. I write a code forced to speak . Along the way it adds a message to the variable $arrMensaje, which is printed at the end to tell you what happened in the code. I call this principle controlled code . I believe that the programmer should never write code that fails without him knowing why it fails. Here he will tell you anything.
3. For the code to work, you need to check a few things, for example your column IDis all capitalized?. Note that table and column names are case sensitive . Well, if you have it misspelled you will know, the code will tell you.
4. Also, when doing the binding, you need to confirm if your column IDis of type VARCHAR in the database or if it is numeric...

With that said, here we go. I hope you can try it and comment the result:

<?php

    session_start();
    require 'conexion.php';

    $nombre = $_POST['nombre'];
    $emai   = $_POST['emai'];
    $pass   = $_POST['pass'];
    $tel    = $_POST['tel'];
    $dir    = $_POST['dir'];
    $id     = $_SESSION['usuario']['ID'];

    // Create connection
    $conn = new mysqli($servername, $username, $password, $dbname);

    // Check connection
    if (!$conn) {

        $arrMensaje=array("mensaje"=>"Error: Fallo de conexión");

    }else{

        if (isset($_SESSION['usuario'])) {

            $strSQL = "UPDATE Usuarios SET name=?, email=?, password=?, phone=?, address=? WHERE ID=?";      
            $stmt=$conn->prepare($strSQL);


            if ($stmt){

                $stmt->bind_param("sssssi", $nombre,$emai,$pass,$tel,$dir,$id);

                if ($stmt->execute()) {
                    $intFilas=$stmt->affected_rows;  
                    $arrMensaje=array("mensaje"=>"Actualizado. Filas afectadas: ".$intFilas.PHP_EOL."Sesión: ".$_SESSION['usuario']['name']);

                }else{

                    $arrMensaje=array("mensaje"=>"No se cumplieron los criterios o clave duplicada " . $stmt->error);
                }

            }else{

                $arrMensaje=array("mensaje"=>"Error: La consulta falló No Error: ".$stmt->errno . "Causa: " . $stmt->error);            
                $stmt->close();
            }


        } else {

            $arrMensaje=array("mensaje"=>"No hay sesión de usuario");

        }

        $conn->close();

    }

    echo $arrMensaje["mensaje"];
?>