It's not at a stupid question at all; actually it's not that straightforward.
Early talent selection programs for children try to gauge the child's natural sensitivity to pitch and rhythm (with simple assignments such as "find the note that has just sounded", "sing this song" or "clap this"). They are also looking at the child's natural ease at the instrument, how relaxed s\he is and how pliable the hands are. The teachers also somewhat subconsciously look at how "teachable" the child is, in a rather narrow understanding: how quickly s\he picks up instructions and adjust to the particular teacher's personality. So, the initial screening is for a person who is sensitive to sounds, a quick study, and compliant. Afterwords, it's judging how well and quickly the child progresses early on.
From what I've seen in music education, I don't think those early selection programs work. Meaning, they are not superior to non-selective programs that accept everyone who is interested, and then lets people self-sort based on motivation and actual achievement. I believe that the original Suzuki institute in Japan has years of stats on that. They are a non-selective program whose graduates go into professional musicianship in very high numbers.
With voice, they would do a similar thing: trying the person's voice range (how high or how low can you go), voice mobility and a good ear (how well you accurately you can repeat a sequence of notes), and listening for the voice's overall tone, volume and tembre. These seem like more objective measures, but they are also for a more narrow task, it's not simply selecting for an aptitude to music but also for a quality of the physical instrument -- the voice -- that is going to make this music.
Advanced programs select on proficiency, not talent.