This sentence gives background information to the story. John is telling readers that he was there and that we can trust what he has written. (See: [[rc://en/ta/man/translate/writing-background]])
To "testify" means to tell about something that one has seen. Alternate translation: "has told the truth about what he has seen" (See: [[rc://en/ta/man/translate/figs-explicit]])
Here "believe" means to put one's trust in Jesus. Alternate translation: "so that you will also put your trust in Jesus" (See: [[rc://en/ta/man/translate/figs-explicit]])