The provider is able to change the settings through two primary methods.
1. DOCSIS configuration file - this is the file your modem downloads when it comes online and includes settings like your speeds (Upstream/Downstream service flows) and it also includes the SNMP settings (used for #2).
2. SNMP - The MSO can also remotely monitor and change your modem via SNMP. There is a large number of DOCSIS MIBs that every cable modem must support in order to get certified and there are also vendor specific MIBs that a modems manufacture will add to support specific features of that modem.
Without SNMP it would be very difficult to maintain a cable network. Other types of access networks have similar features.