Uses of the Imperfect Subjunctive

One of the most common uses of the imperfect subjunctive is in a si clause. In such a clause it has a hypothetical meaning.

Si yo fuera el presidente... - If I were the president...
Si tuviera mucho dinero... - If I had a lot of money...
Si hablara cinco idiomas... - If I spoke five languages...

Another common use of the past subjunctive is in the same situations that you would use the present subjunctive: persuasion, doubt, or value judgement. If the verb in the main clause is in the past, the subordinate clause will use the past subjunctive.

El jefe quería que fueras a la junta.
The boss wanted you to go to the meeting.

No me parecía muy seguro que soltáramos desde ese precipicio alto.
It didn't seem very safe to me that we jump from that high cliff.

Estuvo bien que trabajaras las horas extras.
It was good that you worked the extra hours.

Me gustó que Mario viniera a la fiesta.
I liked it that Mario came to the party.

Esperaba que Juan viniera a la fiesta.
I was hoping for Juan to come to the party.

Me gustaría que Sam viniera a la fiesta.
I would like it for Sam to come to the party

The imperfect subjunctive can also be used to express a polite request or desire.

Quisiera comprar este libro.
I would like to buy this book.