[来る → きて] + いる
The ~ている form expresses ongoing actions ("is doing") and resulting states ("has done" / "is in a state of"). It is one of the most fundamental grammar patterns in Japanese.
When used with action verbs, ~ている describes something that is currently happening, similar to English "-ing."
When used with verbs that describe instantaneous changes, ~ている expresses a state that currently exists as a result of a completed action.
In these cases, the action itself (opening, marrying) has already finished, and ~ている describes the current condition.
The verb しる知る means "to come to know." To express "I know," Japanese uses しっている知っている – the state of having come to know something.
In casual conversation, ~ている is often shortened to ~てる.
The いる part conjugates normally as a る-verb: