The 'Order' column allows you to specify in which order you want the rules to be applied. If you have multiple rules with the same 'Order' value, they get applied in the order they appear in the 'Define Rules' page; but if you specify a value for the 'Order' field, rules with a lower 'Order' value will be applied before rules with a higher 'Order' value. This is very useful, for sometimes an email might trigger several rules. In that case it's important that you have the 'Order' set up correctly.
For example, if you want to filter all mail containing 'Foo' in the subject to Folder A, and you want all mail from 'Bob' to be filed in Folder B you'd make two rules for that (Subject 'Foo' into folder A, and From 'Bob' into folder B). This would work perfectly until Bob sends you an email with 'Foo' in the subject. Now what? Well, in that case it would be smart to have the Order working. If the rule to file mail from 'Bob' into the folder B has the lower Order value, your mail will end up in folder B. Similarly, if the rule to file mail with 'Foo' in the subject into folder A has the lower Order value, your mail will end up in folder A.