To be at a meeting casts the meeting as an attended event; he has gone to attend the meeting, as at implies "elsewhere, not here". If the meeting is in a room a few feet away from the speaker, in a room whose door she can see, the speaker will not say He is at a meeting (except when lying perhaps). If he should open that door and emerge, the listener might well say I thought you said he was at a meeting?
To be in a meeting casts the meeting as something in which one participates either as a speaker or auditor. The preposition in is silent with respect to distance from the speaker's location.
The definite article indicates that the speaker is referring to a particular meeting, and that the speaker assumes the listener knows which meeting that is.