A language parent is a single native speaker you choose to model your speech after. By focusing a large portion of your listening time on one person, you absorb every detail of their speaking style — pronunciation, rhythm, intonation, word choice, mannerisms. Your brain's natural mimicking ability takes over and shapes your output to sound like theirs.
So far, your input has come from hundreds of different speakers, each with a distinct style, dialect and accent. When you start speaking, your output might be a mix of all of them — a bit incoherent, like a patchwork quilt of different people's speech patterns. This is especially true for languages spoken in many different countries (or in one massive country).
A language parent gives you a single, coherent target. Instead of asking "Do I sound good?" (which is nebulous — even every native sounds different), you can ask "Do I sound like this specific person?" That's a much more actionable question.
Over time you'll develop your own style and idiosyncrasies, but starting from a coherent base makes the whole process smoother.
Your parent needs to have a large volume of unscripted, unedited content — at least several dozen hours. Raw content is critical because it shows how they truly speak: every stutter, quirk, verbal tic, and natural pause. For this reason, actors are actually poor choices. Most of their speech is in highly scripted settings or interviews.
You also want to have a large enough sample of solo content (with no one else inturrupting or speaking) so that you don't need to keep jumping around in a video.
Ideally they also have video footage so you can observe facial expressions and body language, which are part of natural communication.
If you can't find someone with that much raw content, it's OK to supplement with some scripted content. And if no single person checks every box, using two parents is perfectly acceptable.
Phase 3 (Listening): This is the best time to start looking for a langauge parent. You can spend a lot of time listening to different people and find the ones that you like the most. And the unscripted listening practice will help a lot with the goals of this phase.
Phase 4 (Speaking): Start mimicking their speech through Chorusing — listen to short clips and repeat until you sound like them. You can also practice continuous shadowing: listening to your parent in real time and speaking along with them.
Phase 5+ (Accuracy and beyond): By now you should be able to understand your parent effortlessly. Use them as your reference point for natural speech. When in doubt about how something should sound, think about how your parent would say it.
Your language parent is a launching pad, not a cage. As you develop comfort and confidence, your speech will naturally evolve into your own style — just like native speakers develop their own voice over time even though they started by copying their parents and teachers. The parent just gives you a strong, coherent foundation to build from.