Usando PHP para cargar el archivo y agregar la ruta a la base de datos MySQL

Primero debes usar print_r($_FILES) para depurar, y ver lo que contiene. :

tu uploads.php se vería como:

//This is the directory where images will be saved
$target = "pics/";
$target = $target . basename( $_FILES['Filename']['name']);

//This gets all the other information from the form
$Filename=basename( $_FILES['Filename']['name']);
$Description=$_POST['Description'];


//Writes the Filename to the server
if(move_uploaded_file($_FILES['Filename']['tmp_name'], $target)) {
    //Tells you if its all ok
    echo "The file ". basename( $_FILES['Filename']['name']). " has been uploaded, and your information has been added to the directory";
    // Connects to your Database
    mysql_connect("localhost", "root", "") or die(mysql_error()) ;
    mysql_select_db("altabotanikk") or die(mysql_error()) ;

    //Writes the information to the database
    mysql_query("INSERT INTO picture (Filename,Description)
    VALUES ('$Filename', '$Description')") ;
} else {
    //Gives and error if its not
    echo "Sorry, there was a problem uploading your file.";
}



?>

EDITAR: Dado que esta es una publicación antigua, actualmente se recomienda encarecidamente usar mysqli o pdo en cambio mysql_ funciona en php