Avery is an English surname turned given name — from the Old French Auvery, itself from the Old Germanic Alberic, meaning "elf ruler" or "wise counsel." The same root that gives Aubrey, Albert, and the medieval king of the dwarves Alberic.
Avery is unisex but used overwhelmingly for girls in the U.S. since the 2000s.
Avery does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
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In Pythagorean numerology the letters of Avery reduce to 8, The Visionary. This is a traditional interpretive system, not a factual claim about the name.