What did Moshe answer?
Rashi: He answered that the people came to him to be judged, in which case he was obligated to sit and the litigants to stand.
Ramban: The reason that they had to stand long hours by him was because he had to deal with so many issues - including Davening for the sick, and that the owners should find their lost articles, 1 litigating their disputes, and teaching them Torah.
Seforno: He explained to Moshe that he was so busy seeing to the multiple needs 2 of the communal leaders that he did not have time to see to tend to the general public until the evening.
Rashbam: He had to bring all their problems before Hashem, and there was nobody else who had access to Hashem.
In order (a) to deal with the communal issues regarding encamping and the likes ("Lidrosh Elokim"); and (b) to settle their interpersonal quarrels which they inevitably brought with them ("ve'Shafat'ti ... "), and (c) to teach them Torah ('ve'Hoda'ati ... "), since they had to be taught before the rest of Yisrael - as the Gemara in Eruvin (54b) explains, based on the Pasuk in Shemos (34:31).