Think "Proof of Service." eService simply means that the normal-proof-of-service-paper copy that you would serve on a party or entity can be served via an electronic service address rather than via a postal service provided that the party or entity agrees to accept electronic service delivery. (Cal. Rules of Court, rule 8.78(a), (f).)
There are two ways to eServe a TrueFiled document: (1) use the TF e-service process during TF filing steps (currently an additional fee of $3 per document); or (2) use your own email to electronically serve the document as an attachment.