Every present, past, and future tense has two different yet parallel ways to say the same thing: the indicative way and the subjunctive way. Each way is called a "mode".
hubiera or hubiese hablado
hablare(not commonly used)
he will have
hubiere hablado (not commonly used)
hubiera or hubiese comido
comiere (not commonly used)
he will have
hubiere comido (not commonly used)
The conditional (what someone would do or would have done under certain conditions or circumstances) is not the present, the past, or the future, and therefore it is not a verb tense. Traditionally, it is considered its own mode: the conditional mode, and therefore it does not have a parallel subjunctive way to say it.
Despite what you may have heard, the subjunctive forms have the same basic meanings as the indicative forms: for example, "comes" and "comas" both mean "you eat".
The subjunctive forms are primarily used in one sentence that is embedded into another, in other words a sub-sentence, or a "subordinate clause". However, the indicative forms also are used in the subordinate clauses, and the confusion arises when you have figure out which one to use.
There are many clear-cut contexts in which one is correct and the other is not, but there are also many contexts in which both are correct, and the difference in meaning can range from slight to significant.
As an English-speaker learning Spanish, even at quite an advanced level, you should be concerned about (and tested on) the clear-cut contexts. Complicated explanations of the nuanced examples are often mistakenly used to explain the clear-cut examples, when those explanations really don't apply.
Most textbooks in English call this the "subjunctive mood", but it originally was called the "subjunctive mode", meaning the subjunctive way to say the same thing. This mispronunciation mistake took hold in English in the early 1900's, and which propagated many subsequent misunderstandings that erroneously associate some kind of emotional and/or unreal significance with these forms.
In Spanish, Italian, French, Portuguese, German, and Latin, the word "mode" is still used.
While the subordinate clauses are strongly associated with the subjunctive forms, the indicative forms are frequently used in subordinate clauses, too. And in a few cases, the subjunctive forms even find their way into the main clause.
MATCH IT - INDICATIVE WITH CORRESPONDING SUBJUNCTIVE