"In network" means the doctor or location has a contract with insurance regarding payment rates and other details of coverage. Typically, this contract will also include provisions such as no "balance billing", where the doctor can charge you more than your insurance thinks is acceptable, requiring you to foot the bill.

A doctor or location "accepting" insurance means they are willing to bill the insurance directly. A location not accepting your insurance does not mean your insurance won't cover the work, but merely that you'll need to pay the doctor directly and file a claim with the insurance to be reimbursed.

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Presuming the US: There are also a few specific laws in place, such as insurance having to treat all emergency care as "in network" and balance billing being disallowed for such care. You also cannot be billed as "out of network" if you go to an "in network" facility and are treated, fully or partially, by an out of network provider, unless you are reasonably warned ahead of time that the provider is out of network.