Not exact translation, but:
The SIM card contains information that allows it to negotiate with available cells regarding which cells and with what parameters it can connect.
The cell relay network (NodeB/RNC/etc) the connection to their owner service which sets up authentication with the SIM card - either by consulting service's "phone number database" based on the IMSI number of the SIM card, or by forwarding it to roaming peer's database (HLR). Then it keeps tunnels between phone and appropriate gateway.
SIM provides the identity of the "account/connection".
IMEI provides the identity of the actual terminal (arguably a bit like MAC address) - called "User Equipment" in UMTS/LTE/5G
BTS/NodeB/RNC/etc. - the radio segment - BTS/NodeB/ENodeB being the "base stations" and RNC is the radio controller (also called Mobile Management Entity in newer standards) which handles setting up connectivity from UE over NodeB to appropriate gateways (connecting to IP network or circuit switched phone networks)
HLR/HSS - Home Location Register / Home Subscriber Server - the part of the system that authenticates the subscriber identified by SIM. It's what maps the connection to right entity in network (to route phone numbers, match billing, etc.) - when you use roaming, the RNC/MME is set up in a way where it can find your original HLR/HSS (tackling extra fees as necessary)
gateways - different depending on version of network as well as whether you use IMS-only network (aka VoLTE/VoNR, in actuality part of 3G known better to people here as VoIP/SIP), or whether circuit switched fallback is used (operates purely on 2G and 3G, with latter being added in later revision).