Peter connects love to a changed life: “Having purified your souls by your obedience to the truth,” they are to have sincere brotherly love (1 Peter 1:22). He describes the love as earnest and “from a pure heart” (1 Peter 1:22).
In 1 Peter 1:22–25 Peter urges his readers to practice intense, heart-level love within the community. He grounds that command in what has already happened to them: they have been cleansed as they aligned themselves with “the truth,” and they have received a new kind of life. This paragraph closes a larger opening section that begins with living hope and a new identity (1:3–12) and then turns to how that identity shapes conduct (1:13–21).
This paragraph connects community love to a prior change in the readers. Peter treats them as already “purified” and ties that to “obedience to the truth,” with the Spirit involved in the process (explicit). From that new reality he points to a concrete result: sincere family-like affection, and then a call to intense, heart-level love (explicit).
A careful answer keeps the immediate passage, the book's argument, and the whole-Bible storyline together, so the question is answered in context instead of as a detached idea.
Start with 1 Peter 1:22, then read the surrounding section so the answer stays connected to the passage's flow.
22Seeing you have purified your souls in your obedience to the truth through the Spirit in sincere brotherly affection, love one another from the heart fervently: