The Summon response window is an unofficial term for the activation timing of cards that respond to the Summon of a monster(s), such as "Trap Hole" cards, "Torrential Tribute", etc. There is up to one chain in the "Summon response window". As from this timing, the Summoned monster is considered successfully summoned. Their Continuous Effects immediately applies.
When a card or an effect is activated during this timing, it is considered to be activated in response to both the Monster's Summon and the preceding Chain Link.
For an Inherent Summon, this timing is after the Summon negation window. For a Summon by card Effect, this occurs immediately after the monster(s) are Summoned. Cards like "Solemn Warning", "Solemn Judgment", etc. that negate the Summon of a monster cannot be activated during this timing; they can only be activated in the Summon negation window. Summon Response Window would miss its timing if the Summon is not the very last thing in the chain.
During the Summon response window, due to Fast Effect Timing, first the turn player must activate any compulsory effects that they triggered, such as "Summoning Curse" and "Summoner Monk", then their opponent must do the same. Then, the turn player has the opportunity to activate optional effects like "Torrential Tribute" and "Armageddon Knight"; if the turn player passes, then the opponent also has the opportunity to activate these effects. If at any point either player starts a Chain, standard Chain rules are followed.
The turn player attempts to Summon "Black Luster Soldier - Envoy of the Beginning", banishing 1 DARK and 1 LIGHT monster from his/her Graveyard. The Summon was not negated, so the Summon response window is now open, and the turn player can activate cards in response to the Summon of a monster. If the turn player passes doing so, then the opponent may do so.
If both players pass without responding to the Summon, nothing happens and the game state becomes open again.