And loosen the knot from my tongue, that they understand my speech.
This is referring to the lisp that he had.
This lisp was a result of an incident when he was presented a date and a hot coal stone and he placed the coal on his tongue instead of the date. A detailed explanation of this story is forthcoming in the following chapters.
However, he did not ask Allah to remove this affliction all together. Rather, he asked for removal of his stammering so the people would understand what he intended in his speech. He was only asking for what was necessary to deliver his message. If he had asked for the removal of his affliction in its entirety, it would have been cured for him. However, the Prophets do not ask for any more than what is required. Therefore, he was left with the remnants of this accident that took place with his tongue. Allah informed of what Fir`awn said concerning him,
أَمْ أَنَأ خَيْرٌ مِّنْ هَـذَا الَّذِى هُوَ مَهِينٌ وَلَا يَكَادُ يُبِينُ
Am I not better than this one who is despicable and can scarcely express himself clearly! (43;52)
This means that he is not eloquent in speech.
Concerning Allah's statement,
وَاجْعَل لِّي وَزِيرًا مِّنْ أَهْلِي