Mendeleev left gaps in his periodic table because the properties of known elements predicted other, as-yet-undiscovered, elements in these locations. As Mendeleev organized his periodic table, he recognized that these gaps would be filled as future scientists identified new elements.
Mendeleev put together the periodic table on the basis of known properties about atoms, specifically the atomic mass, equivalent mass and valency. This method revealed repetitive, or periodic, patterns among the elements that suggested an inherent organization. In some cases, the measured atomic mass of an atom conflicted with its predicted position in Mendeleev's periodic table. In these situations, Mendeleev correctly assumed that the measurement was wrong, and he successfully estimated the correct atomic mass.
Similarly, Mendeleev predicted the properties of the elements that would fill the blank spaces in his periodic table. For example, he anticipated the discovery of gallium (which Mendeleev called eka-aluminum) as well as several characteristics of this element. He quite accurately estimated features such as the atomic mass, density, valency and even the method of discovery of gallium. His predictions were similarly impressive in predicting the discovery of scandium, germanium and other elements; however, his predictions were not uniformly accurate. In at least three cases, the gaps in his table did not lead to the discovery of a new element.