Written mostly for people arranging one of these at an office, or for a family whose vocabulary has drifted a generation from it. Nothing here is complicated; it is just rarely written down.
the gathering
Baithak — literally a sitting. An informal musical gathering where everyone is seated on the same level and there is no separation between performer and audience. The word carries the informality: it is a sitting, not a show.
Satsang — a gathering in the company of truth or of good company, depending who is translating. Broader than a baithak, and not necessarily musical, though it usually is.
Bhajan sandhya — literally an evening of bhajans. Used for a gathering built specifically around devotional singing, usually at home.
Kirtan — call-and-response devotional singing, generally more rhythmic and more participatory than a bhajan. In practice the line between the two is blurry and nobody minds.
the music
Bhajan — a devotional song. The form is loose; what makes something a bhajan is its subject and its use, not its structure.
Dhun — a short repeated phrase or refrain, sung over and over, often building in tempo. This is usually what a room is singing when it sounds like everyone knows the words. They may not; a dhun teaches itself in two repetitions.
Call and response — one voice sings a line, the room repeats it. The engine of congregational singing, and the reason nobody needs to know the material beforehand.
Taal — the rhythmic cycle underneath the music. Relevant to you mainly because it is what the room is clapping along to.
Aarti — the ritual of light, usually sung, often with a lamp circled before the deity. Frequently the opening or closing point of an evening, and a natural anchor for scheduling music around.
the instruments you are likely to see
Harmonium — the small hand-pumped reed organ, played seated. The default melodic accompaniment for devotional singing across most of India.
Cajon — a wooden box drum the player sits on. Increasingly common in smaller line-ups because it is portable, needs no tuning and works unamplified in a room.
Dholak and tabla — traditional hand percussion, both played seated. Warmer than a cajon and more tonal.
Octapad — an electronic percussion pad. Used where a fuller or louder rhythm section is needed than hand percussion can provide, typically outdoors or on a stage.
Manjira and kartal — small hand cymbals and wooden clappers. Often passed around, and the easiest way to get a room participating physically.
the practical words
Prasad — food that has been offered and is then shared. Served after the music rather than during, unless you want the room to empty.
Toran — the hanging strung across a doorway, usually marigold and mango leaves. The cheapest way to make an entrance feel like an occasion.
Rangoli — the floor pattern at the threshold, in powder, rice or petals.
Diya — the oil lamp. Does more for the atmosphere of a room than any electric light, and the single most effective thing on this list.
Muhurat — an auspicious time window, fixed by the calendar rather than by convenience. If your gathering has one, everything else in the schedule moves around it.