Mönlam is intrinsically an aspiration or wish. Since Buddhism deals with mind as a primary factor in the pursuit of wellbeing and enlightenment, it is important to have the right kind of aspiration or intention. Words and texts which help us generate good aspiration and motivation are also referred to as mönlam.
Buddhist mönlam are mainly mental aspirations rather than just prayers or supplications to a powerful or superior being. When one does mönlam, one aspires, intends or wishes to do something, be someone or reach somewhere. So Buddhist mönlam involves having a strong and earnest wish.
The most common theme of Buddhist mönlam is to wish to reach enlightenment, which the supreme goal of all endeavours, and also to obtain happiness and wellbeing before reaching enlightenment. So Buddhist prayers are aimed at the dual goal of reaching enlightenment ultimately and of attaining happiness and minimizing suffering in the interim.