According to the Catholic Church, demons are simply fallen angels: i.e., angels who have sinned gravely against God and are now living the eternal consequences of their separation from Him.
Angels are creatures that, like us, are persons (that is, they are capable of intellectual knowledge and free acts of love). However, unlike us, they are not limited by corporeity—that is, they are pure spirits and have no bodies. In the words of the Catechism of the Catholic Church (CCC),
As purely spiritual creatures angels have intelligence and will: they are personal and immortal creatures, surpassing in perfection all visible creatures, as the splendor of their glory bears witness (No. 330).
According to nature, therefore, angels are much mightier and more noble beings than we are.
The fallen angels, also called demons
Like us, angels are submitted to a kind of trial, in which they may choose to serve God for all eternity and enjoy the Beatific Vision, or else they may refuse to serve Him and be forever deprived of His presence. Those angels who chose the latter course are the “fallen angels,” also known as “demons.” As the Catechism puts it,
Scripture speaks of a sin of these angels. [The reference is to 2 Pet. 2:4.] This “fall” consists in the free choice of these created spirits, who radically and irrevocably rejected God and his reign. We find a reflection of that rebellion in the tempter's words to our first parents: “You will be like God.” [Gen. 3:5] The devil “has sinned from the beginning” [1 Jn. 3:8]; he is “a liar and the father of lies” [Jn. 8:44] (No. 392).
The Devil, or Satan, is simply the chief of these rebellious angels:
Behind the disobedient choice of our first parents lurks a seductive voice, opposed to God, which makes them fall into death out of envy. Scripture and the Church’s Tradition see in this being a fallen angel, called “Satan” or the “devil”. The Church teaches that Satan was at first a good angel, made by God: “The devil and the other demons were indeed created naturally good by God, but they became evil by their own doing” [Lateran Council IV (1215): DS 800] (No. 391).