A conditional sentence in English uses "if" to indicate that one state or act is conditional upon the occurrence of another state or act: "If it rains, we will stay inside."
Anytime you say "if something, then something ....", you are using a conditional sentence. A conditional sentence has at least two parts. The "if-clause", which describes the conditions that allow something to happen, is called the protasis in formal Latin Grammars. That means that it is something which is "set out first." The main clause, sometimes introduced with "then" in English, is called the apodosis in formal grammar. That means something that is a consequence of the "if-clause": "If you're happy (protasis), I'm happy (apodosis)." There are several different kinds of conditions and, as often in English, our language is not always as precise as classical literary Latin was. This may be the result of the literature that remains and if we had scratchy old wire recordings of Latin children talking about the latest gladiator games, we would probably here a language of great variety, nuance, cliche, and idiom.
Still, Latin Conditions follow fairly strict rules in the Classical Period. I believe that there is some confusion in the discussion of these conditions, and I will try here to make things clearer. You may skip ahead at any point either to the truth about LATIN CONDITIONS or the standard textbook version of Latin Conditions. You should probably know both versions of the story.
You may also follow links to descriptions that attempt to address practical issues: how do you translate Latin Conditions into English or English Conditions into Latin. You need to think about both kinds of translation in order to understand the differences between the languages. There is also a conceptual concern: what relationship is being described by the moods and tenses that are used in Latin. This approach will give you an abstract understanding of the grammar, and with that understanding you can ask youself how you would say the same thing in English. There is also a Table that outlines all the typical conditions in Latin.