Coordination of benefits (COB) is the set of rules insurers use to decide which plan pays first when you're covered by more than one health plan, and how much a second plan puts toward what's left.
Not every plan works this way. Most individual marketplace plans don't coordinate benefits the way employer plans do. Some will coordinate with Medicare or a group plan, but that depends on state rules and your specific policy, so it's worth checking your Summary of Benefits.
When two plans do coordinate, COB rules make one plan primary and one secondary. The primary plan pays first, up to its normal limits, and the secondary plan only looks at what's left after that. If you have your own plan (like one you picked through Thatch) and you're also covered as a dependent on a spouse or partner's group plan, your own plan is usually primary since you're the policyholder there, while the plan where you're a dependent is typically secondary.
Being secondary doesn't mean you get much extra, though. A secondary plan only pays what it would have paid if it were primary, minus what the primary plan already covered. On a $1,000 bill, if your primary plan pays $700, your secondary plan checks what it would have paid as primary. If that number is close to $700 too, you likely won't see anything more.
That's part of why having two plans usually isn't worth it. Two plans rarely add up to more coverage, and they mean two premiums, more paperwork, and slower claims while insurers sort out who pays what. It can be worth it if you have complex medical needs that benefit from extra coverage, or if the second plan doesn't cost you anything.
This is general information. Check your Summary of Benefits or contact your insurer to see exactly how your plans coordinate.