What was Esperanto originally for? Or why is Esperanto used for?
The question is simple enough to be understood, but I really want to know why is Esperanto useful.
My suggestion would be to google this question, read some of the replies, and then come back to ask any specific questions that come to mind.
Here are two videos I made (one year and two years ago) to attempt to answer these two questions.
Long story, short. The original idea was, people who spoke a different language could speak to each other in the same common language.
Making friends, spreading peace, having fun, language equality, learning other cultures, mental exercise, etc.
To answer "What was Esperanto originally for?" I direct you to the introduction of "Dr. Esperanto's International Language." This book was the first one published detailing Esperanto. At the time, it was simply referred to as "the international language," having not yet been given its name. (Dr. Esperanto's International Language, Introduction https://en.wikisource.org/wiki/Dr._Esperanto%27s_International_Language/Introduction)
While the entire introduction is an answer to your question, the best summary might be the listing of the 3 "principle difficulties" that were the original intention of Esperanto to solve.
"1) To render the study of the language so easy as to make its acquisition mere play to the learner.
"2) To enable the learner to make direct use of his knowledge with persons of any nationality, whether the language be universally accepted or not; in other words, the language is to be directly a means of international communication.
"3) To find some means of overcoming the natural indifference of mankind, and disposing them, in the quickest manner possible, and en masse, to learn and use the proposed language as a living one, and not only in last extremities, and with the key at hand."
And in answer to "why is Esperanto useful?" there are many possible responses. The four strongest, in my opinion are:
1) Several studies have concluded that Esperanto has advantages in teaching the learner about language learning in general (the technical name for this is "propaedeutics"). So, if you want to learn other languages, spending some time on Esperanto can be helpful. I like to say it is similar to a vaccination, in that, like how giving your body a weaker version of a virus teaches it how to fight that virus, giving your mind a weaker version of a foreign language teaches it how to tackle the problem of learing a foreign language. (Propaedeutic value of Esperanto https://en.wikipedia.org/wiki/Propaedeutic_value_of_Esperanto)
2) Esperanto's speaking community is very inviting. It is not much of an exaggeration to say that I start off as a friend with anyone else who speaks Esperanto. The tight-knit nature of the community, combined with its original motivations of international friendship, make its speakers natually friendly to other speakers. I can chat with just about anyone on an Esperanto IRC channel or on Amikumu and the odds are high that they are a nice person, just looking to chat, and that they will be thrilled to talk with me.
3) Esperanto grants you access to new media. While Esperanto's speaking community is small, it produces a fair amount of magazines, blogs, YouTube videos, podcasts, music, etc. The news articles in particular interest me, as it allows me to get a non-English perspective on how people view current events.
4) It gives you the benefits of knowing a second language in a fraction of the time. All the cool stuff that comes along with knowing a foreign language can be yours in just a few months of relatively small effort. I will concede that learning any language, even Esperanto, is a decent time commitment, but compared to a language like French or Spanish, Esperanto is a breeze to learn. I was able to carry on a conversation in just 8 months of less than 20 minutes of study a day, on my own. Compare that to French, where 4 years of proper high school study didn't get me anywhere.
Now, what "cool stuff" do I mean? All the little things that come along with knowing a second language: Being able to sit at a table in a restaurant chatting away in a language that only those at the table know, noting that people at the next table are intrigued, and having the waiter ask "What language are you speaking?" when they bring the check. Watching a YouTube video on your phone when on break only to have your co-worker overhear, give you a surprised look, and ask "You understand what that guy's saying?!" Or saying something ludicriously obscene when you stub your toe, only to have your family just give you a raised eyebrow instead of being offended because they don't realize what you just dared to say out loud.
That last reason is, admittedly, sort of narcissistic, but it's a real motivation for some people. And yeah, it's cool. ;)
Evildea (Richard Delamore) on YouTube, answered your question in one of his videos, and his motivation for learning was similar to point 4. At 1:49 he says: "I've always wanted to learn a language. It [learing Esperanto] made me feel cultured... I always felt that someone who spoke another language was cultured." (Is Esperanto Useful? https://www.youtube.com/watch?v=Mf83hCF5Cxg)
If these things do not appeal to you, then I will admit that there isn't much of a "practical" reason to learn Esperanto. Unlike Spanish or Chinese, it won't open many doors to jobs, nor does it give you the ability to go to a specific foreign country and talk to anyone in the street. However, I do feel it has benefits and, if these things interest you, I think it is worth the time to learn considering how little time (again, compared to other languages) it actually takes.
I know it sounds odd, but learning Esperanto will improve all your other langauges! It is just about the only one where you can just open up and try it without worrying about whether or not you are "good enough."