Only Platypus and Echidnas (there are a few species) lay eggs. Monotremes are considered mammals because they have fur, are at least partially endothermic (warm-blooded), and secrete milk for their young. Interestingly, monotremes do not have nipples, but simply secrete the milk through pores in their skin - the babies lick the milk off of their fur.
Echidnas also have a pouch, like a marsupial, and a single cloaca for expelling waste and reproduction, (like a bird or reptile) instead of a separate urethra, anus and genital tract like most other mammals. (Marsupials have a combined urethra/anus as well, but have a separate reproductive tract).
Platypus, being largely aquatic, do not have a pouch.