Translation:I thought that you wanted to go to the balcony.
"Quisesse" is in the subjunctive mood in past tense.
It happens because of the construction "pensar que" in past. A couple of verbs suggesting uncertainty will ask for the subjunctive tense after it.
- Pensar, acreditar, querer, preferir and others.
Normally, with pensar and acreditar, it's possible to use "queria" instead. But it's not always possible to replace the subjunctive with the imperfect past.
- Queria = Pretérito imperfeito do indicativo (Imperfect Indicative)
- Quisesse = Pretérito imperfeito do subjuntivo (Imperfect Subjunctive)
Imperfect Indicative = It means the facts have not been fully completed. They are continuous, but not completed. Example: Ele trabalhava muito durante os fins de semana.
Imperfect Subjunctive = It expresses a fact that has already passed, but that happened after another fact. It is also used in sentences which one expresses the idea of condition or desire. Examples: Se ela ganhasse na loteria, compraria um carro. | Eu esperava que ela ganhasse a eleição.
When "pensar" is in the past tense, the verb in the subordinate clause is often conjugated in the subjunctive mood.
The subjunctive can be used to soften an order to be polite, or it can indicate that what you expected to happen didn't take place.
Eu pensei que você quisesse ir para a sacada...mas [você] mudou de ideia.
The "correct" answer is wrong. In English you do not go "to" a balcony, you go "on" a balcony. Yet again, an English answer provided by a Portuguese speaker without being checked by a native English speaker.