Clearly its A mark of great respect/love/belief or close ties with amer.
A fearsome battle was fought in Gujarat, where akbar life was once again rescued by bhagwant das and man singh.
(previously bhagwant das saved akbar's life in battle of paronkh, as shown in the show.. the battle is true..!!it happened really. bhagwant das took a bow shot on akbar on his body and also offered him his water. Paronkh - is a village in today's uttar pradesh, in eta district.)
They(man singh and bhagwant das) arrived in time with reinforcements. Young prince Man singh led the army and bhagwan das fought/stood, side by side with akbar in entire battle. A force of 3000 warriors comprising some mughals and mostly rajput warriors defeated a force of 20,000 afghans!!! Shocking but true. Akbar recounts it in his memoirs as one of the most important battles in his life. this changed his attitude towards rajputs considerably.
In this battle, the raja's elder son, Bhupat Rai/ Bhupat Singh was killed.(They have not shown him in the serial till now, hope they will introduce him also.) Akbar made bhupat's killing a personal issue, and allowed Maryam Zamani to go to Amer for mourning Bhupat's death. Again, the outcry of mughal maulvis and ulemas and nobles was severe, as they indirectly accused akbar of giving large freedom to his hindu wife. But akbar again defied them and allowed her to go.
Now, he launched a manhunt for shah madad, foster brother of muhamed Husain mirza, who had killed bhupat. He was caught and personally beheaded by akbar.!!
Clearly, these events show that amer had great meaning in this life. But, akbar was such a big personality, that a lot has been written about him, his wars, but not about his personal life.