I am assuming you already have some knowledge of setting up the observer and controller, but let me know if that is not the case, and I will expand my answer.
In the observer (app/code/local/Package/Vendor/Model/Observer.php):
if($session = Mage::getSingleton('customer/session')) {
$session->setData("some_variable_name");
}
In the controller (path will vary):
if($session = Mage::getSingleton('customer/session')) {
$passed_value = $session->getData("some_variable_name");
}
// do something with $passed_value