Theria is a grouping of Eutheria (placental mammals) with Metatheria (marsupial mammals), specifically excluding Prototheria (egg-laying mammals, AKA monotremes). This is done if one believes that placental mammals and marsupial mammals are more closely related to each other than they are to the egg-laying mammals.
Of course, there are biologists that believe that this is not the case, and so there is also an alternate subclass, Marsupionta, in which marsupials and monotremes grouped together, and the eutherians are the odd ones out. Your taxonomy can include theria, marsupionta, or possibly neither, but it cannot contain both.
Therians are viviparous (give birth to live young), without using a shelled egg. They have external ears, can suckle on a nipple, and have an ankle specialized for power and range of motion. They are often classified by their specialized dentition. The only currently extant mammals that are not therians are the platypus and the echidnas (AKA spiny anteater).
The word 'theria' comes from the Greek word meaning 'beasts' or 'animal'.