Can anyone explain what TFR's are supposed to do?

The TFRs are supposed to prevent an unspecified attack on the President of
the United States by unspecified persons.

While it is true that the TFRs are probably ineffective and they are
discriminatory, it is not true that general aviation airplanes pose no
threat or that their threat is less than that of ground vehicles.

A small airplane can approach a target at speeds in excess of 200 mph and
drop a bomb or detonate itself with little warning. The fact that the same
mission could be accomplished by other means, such as a truck full of
explosives, is irrelevant. It is possible that the means of attack is more
important to the attacker than the effectiveness of the attack -- the whole
"terror from the skies" thing.

Small airplanes flown by the Civil Air Patrol carried bombs and were
effective during WW II in patrolling against submarines and even managed to
sink one.

As Lee Harvey Oswald demonstrated, there is no way to protect the President
or anyone else against a determined and possibly suicidal attacker. There
will always be people who are willing to take great risks to get close to
the President, although no one has made a serious attempt since Gerald Ford.