Homoousios (from Greek ὁμός/same + "οὐσία"/essence) is a Greek word meaning same substance or same essence. It refers to God's nature ("what God is") as opposed to God's Persons (hypostases; "who God is") or God's attributes ("what God does"). The term "homoousios" denotes that one ousios (nature/essence/substance) is shared by the three Persons of the Trinity.
It is used in the Nicene Creed to say that Jesus Christ is of one essence with the Father. Although it does not appear in the Bible, the fathers of the First Ecumenical Council ultimately decided that this was the best language to use concerning the Holy Trinity.
The competing term at that council was homoiousios meaning "similar essence"; it was favored by the moderates among the Arians, the Semi-arians. Because of how close these two words are in the Greek, it has been said that there was only "one iota" of difference between them.