Short answer: With an embedded deductible, each family member has their own individual deductible inside the family deductible, so one person’s claims can be covered before the whole family amount is met. With an aggregate deductible, the entire family deductible must be met before the plan pays for anyone.
On a family plan, the deductible structure matters a lot. An embedded deductible has two layers: each person has an individual deductible, and once any one member meets it the plan starts paying for that person, even if the larger family deductible isn’t met yet. An aggregate (non-embedded) deductible is a single family amount that must be satisfied (by one person or several combined) before the plan pays for anyone. Aggregate deductibles are most common on HSA-qualified family HDHPs and can mean higher upfront costs if one family member has a big claim.