You can use SOAP API, Integrate salesforce with external system and update or insert data in salesforce.
To integrate Salesforce with external system you need to consume the WSDL from salesforce in your external system.
Access WSDL
You can choose any of the WSDL "Enterprise or Partner" and consume and generate stubs.
You will get the code of all the calls which you can make from external system to Salesforce.
You need to specify the Endpoint URL (The endpoint where you need to make the call).
You need to create a webservice and specify the condition when the records would be updated in Salesforce.
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