If you saw the 'relieved of duty' comment by JG, you saw basically the whole show. After that Bartlett walks out and the show ends.
Why did he step down - temporary mental incapcity to discharge the office of the president. under times of duress or illness, the President may allow the next in command to take over the role of Commander In Chief until such time when he can perform his duties.
Section 3 of the Constitution states: Section 3. Whenever the President transmits to the President pro tempore of the Senate and the Speaker of the House of Representatives his written declaration that he is unable to discharge the powers and duties of his office, and until he transmits to them a written declaration to the contrary, such powers and duties shall be discharged by the Vice President as Acting President.
The situation with his daughter being kidnapped created a situation where he felt his ability to make rational decisions as the president would be compromised with the decisions he would make as a father.
That is why Toby ran up to the White House and said how can we let him stay in his office. Then he clarified his thoughts that said if someone took my new babies I would drop napalm on Yellowstone to get them back.
Bartlett felt he would make decisions as a father, not as a President. And in case any foe did or attempted to do something Bartlett felt he would not be able to respond. So he turned over control to the next in line (since there is no VP) the Speaker of the House.
In case you are wondering, Bartlell said he had 2 letters one to resign and one to reinstate himself. The time to deliver the second one is up to him. His reinstatement can be turned down by the temporary commander in chief PLUS 51% or greater of the cabinet. That won't happen, the cabinet is loyal to Bartless so JG is gone once the situation is resolved.
Sorry for the long winded answer. I had already been through this with my wife.
RU