Della cries for a multitude of reasons when she receives her present from Jim. Emotions can be complicated things, and sometimes a woman's tears are the sum of many layered feelings.
1) Tears of Joy: Della's tears are an outpouring of joy for receiving the combs that she has coveted for so long. She feels overwhelmed by Jim's amazing love and understanding to give her such a beautiful gift.
2) Tears of Grief: Della mourns the loss of her beautiful hair and seeing those exquisite combs has brought back the hard reality of her sacrifice. She will have to wait a while before she can enjoy the combs. Most women would probably shed more than a few tears if they had just hacked all of their gorgeous hair off.
Della's tears are not triggered by any one overriding emotion, but rather the sum of all that she feels about the combs, her love for Jim, and the hardship of their sitation.