This is the imperfect subjunctive one of the most feared tenses in all of spanish.
If you have the book 501 spanish verbs the preface of each tense tells you the exact usage.

Okay, but I thought the imperfect subjunctive was formed from---| 3rd person plural preterite, take off -ron, add -ra, -ras, -ra, -ramos, -rais, -ran.

Where did the -se come from''? Is it like I learned Mexico-Spanish but that's Spain-Spanish or something'

It can be either...as Whit mentioned above, if you get a good grammar book it will explain the two forms of the imperfect subjunctive.

The 'se' endings aren't widely used anymore, you are correct with the other endings, and these are the ones you should learn really, but just be aware of the other way the imp. subj. can be formed

Hi Sarah
The subjunctive is used widely by the spanish. It can in certain circumstances subtlety alter the meaning of the phrase. The examples that you gave, which are the imperfect subjunctive are generally followed by the conditional tense.
Example
Si mi hermano tuviese vacaciones en la misma época que yo, Iríamos a Madrid.
If my brother were to take his holidays at the same time as me, we would go to Madrid.
(tuviese - imperfect subjunctive- were to take)
(Iríamos - conditional - we would go)

There are 2 forms of past subjunctive. In the US we learn 1 form over the other, but it helps to be aware of the other one in case, as you did, come across it in reading.

hablara, hablaras, hablara, habláramos, hablarais, hablaran or

hablase, hablases, hablase, hablásemos, hablaseis, hablasen

Yes, as mentioned, it can be either. That is why it can be annoying to learn this tense. If you just use the endings you know (-ara, -aras, etc.) you will be understood. However, be able to recognize the other form (-ase, -ases, etc.), as it is still occasionaly heard.

Thank you so much everybody for your help. I understand now. It's good to know so I can more fully understand what I'm reading!