when using the mail() function it must be in the form of mail($to, $subject, $message, $headers) where $headers are optional.
Your $to and $subject are fine, but you can't include Age, FirstName, LastName as you have them. Instead, put them into your $message variable.
<?php
$to = "****EMAIL*******";
$subject = "Contest Entry";
$Age = $_REQUEST['age'] ;
$FirstName = $_REQUEST['first_name'] ;
$LastName = $_REQUEST['last_name'] ;
$message=$age." ".$FirstName." ".$LastName;
$sent = mail($to, $subject, $message);
if($sent)
{print "Your mail was sent successfully"; }
else
{print "We encountered an error sending your mail"; }
?>
This will send an email to $email with a subject $subject and the email itself will be Age FirstName LastName