In-Network
This is your insurance company's approved list of doctors or providers. If you use an in-network provider, your costs will usually be lower.
Out-of-Network
These are doctors or providers that aren't on your insurance company's approved list. If you use an out-of-network provider, your costs will usually be higher.
Carve-Out
These are services that are not covered by your insurance at a specific place, even if the place is in-network. For instance, your policy might cover most services at Mt. Washington Pediatric Hospital, but might require you to go elsewhere for services like psychology, rehabilitation or lab tests. In this case, your services here would not be covered by insurance, even though MWPH is in-network.