When a person gives a “testimony,” they tell other people the things they know about something. The person also says that the things they are saying are true.
To “testify” is to give “testimony.” At a trial, a witness testifies about something they saw or experienced. A witness who gives “false testimony” does not say true things about what they saw or experienced.
In the Old Testament, the ark of the covenant was also called the ark of the testimony (see: Exodus 25:22). The ark was called this because inside of it were the stones on which the Ten Commandments were written. The Ten Commandments were God’s testimony or decree to the Israelites that he was making a covenant with them (see: Exodus 16:34; 25:16).
In the New Testament, the words “testify” and “testimony” were often used to talk about the things Jesus’ followers said about him. They spoke the truth about the things that happened in Jesus’ life, death, and resurrection (see: John 1:32-34; 2 Timothy 1:8; Revelation 1:2, 9).