The scientific objectives of neutron mapping of the Moon are presented as 3 investigation tasks of NASA's Lunar Reconnaissance Orbiter mission. Two tasks focus on mapping hydrogen content over the entire Moon and on testing the presence of water-ice deposits at the bottom of permanently shadowed craters at the lunar poles. The third task corresponds to the determination of neutron contribution to the total radiation dose at an altitude of 50 km above the Moon. We show that the Lunar Exploration Neutron Detector (LEND) will be capable of carrying out all 3 investigations. The design concept of LEND is presented together with results of numerical simulations of the instrument's sensitivity for hydrogen detection. The sensitivity of LEND is shown to be characterized by a hydrogen detection limit of about 100 ppm for a polar reference area with a radius of 5 km. If the presence of ice deposits in polar "cold traps" is confirmed, a unique record of many millions of years of lunar history would be obtained, by which the history of lunar impacts could be discerned from the layers of water ice and dust. Future applications of a LEND-type instrument for Mars orbital observations are also discussed.