And speak to him mildly, perhaps he may accept admonition or fear (Allah).
This Ayah contains a great lesson. Even though Fir`awn was the most insolent and arrogant of people and Musa was the friend of Allah among His creation at that time, Musa was still commanded to speak to Fir`awn with mildness and softness. Therefore, their invitation to him was with gentle, soft and easy speech that is used by one who is a close friend. This is so that the message may have more effect on the souls, and so it would have deeper and more beneficial results.
This is as Allah, the Exalted, says,
ادْعُ إِلِى سَبِيلِ رَبِّكَ بِالْحِكْمَةِ وَالْمَوْعِظَةِ الْحَسَنَةِ وَجَـدِلْهُم بِالَّتِى هِىَ أَحْسَنُ
Invite (mankind) to the way of your Lord with wisdom and fair preaching, and argue with them in a way that is better. (16;125)
Concerning Allah's statement,
لَّعَلَّهُ يَتَذَكَّرُ أَوْ يَخْشَى
perhaps he may accept admonition or fear (Allah).
This means that perhaps he will recant from that which he is in of misguidance and destruction,
أَوْ يَخْشَى
(or he will fear), meaning that he will become obedient due to fear of Allah.
This is as Allah says,
لِّمَنْ أَرَادَ أَن يَذَّكَّرَ أَوْ أَرَادَ شُكُوراً
For such who desires to remember or desires to show his gratitude. (25;62)
Thus, to remember means to recant from that which is dangerous, and fear means to attain obedience