your brother and partner: Although separated from other Christians due to imprisonment, John felt a sense of community with them in suffering. This connection was based on hope in God's kingdom and a willingness to endure.
The Roman fortress on the island of Patmos held prisoners and exiles. Patmos was part of a group of islands that protected the busy seaport of Miletus.
because of the word of God and my testimony: These two statements mean the same thing. This is a common pattern in Semitic writing, where the second line repeats or explains the first. By John's time, Jews were convincing Roman authorities that Christianity was different from Judaism and therefore not an authorized religion.