I have seen the business that God has given to the children of man to be busy with. He has made everything beautiful in its time. Also, he has put eternity into man's heart, yet so that he cannot find out what God has done from the beginning to the end. I perceived that there is nothing better for them than to be joyful and to do good as long as they live; also that everyone should eat and drink and take pleasure in all his toil—this is God's gift to man. (Ecclesiastes 3:10-13 ESV)We have "eternity in our hearts" because mankind was designed by God for eternity; at the beginning, we were not created able to die, but since the Fall our bodies aren't ready for eternity. Barring Christ's return beforehand, each of our bodies will one day die and decompose. To our bodies, death is natural enough, but to our designed-for-eternity hearts, death is a completely foreign concept. We hate death deep down in our hearts because our hearts were not designed to comprehend death. Maybe that's part of why we cry and grieve even for departed loved ones that we have every reason to believe are in Heaven now. Our bodies can die, and our minds can understand it when it happens, but our hearts just can't accept the idea of death.
The happy ending is that we do have this life, and God intends for us to enjoy it as fully as we can, and accomplish what we can, even in this short lifetime! You will not be able to accomplish before you die everything that God has planned for you... because there's more than one mortal lifetime's worth of it! And then when our hearts finally meet with God in eternity, He'll have our continuing assignments ready and waiting!