Assuming you are specifying the correct number of fields for your database (as I can't see a field that would equate to a primary key or ID field):
$spacecraft = $POST['spacecraft'];
$category = $POST['category'];
$source = $POST['source'];
$info = $POST['info'];
$string = "INSERT INTO lessons VALUES('$category','$category','$source','$info')";
$insert = mysql_query($string);
If you have more fileds than just the four within your table, ie an auto-incrementing ID field, you also need to specify it within your sql. So assuming the table has 5 fields, the first of which is ID:
$spacecraft = $POST['spacecraft'];
$category = $POST['category'];
$source = $POST['source'];
$info = $POST['info'];
$string = "INSERT INTO lessons VALUES('', '$category', '$category', '$source', '$info')";
$insert = mysql_query($string);