There is an old saying "Don't bite the hand that feeds you", and when I approach the issue of what an "opinion" is, I am treading on thin ice, because opinion, together with videos of cats doing amusing things, is what drives the great and grand internet.
But what is an "opinion"? I am at times a teacher of the GED, and one of the many "critical thinking" skills that is presented on the GED is telling the difference between a fact and an opinion, which is a good skill to have in higher education, but which on the internet is a much less important skill to have than a good source for animated gifs. But in any case, fact vs. opinion is a basic piece of rhetorical knowledge, but upon further investigation, what exactly an opinion is begins to become more hazy. Even setting aside the distance between fact and opinion, there are many different things that are "opinions", many of which do not have much to do with each other. Listed below, in no particular order, and with examples taken at random, are a variety of things that can be called "opinion".
Conjecture: conjecture, or "guessing" is a type of opinion where someone uses known facts to try to figure out unknown facts. "It is raining today, the river will rise" is conjecture, and therefore an opinion. However, the problem with this is that some types of "conjecture" have such a close relationship between cause and effect, that they can be referred to as fact, not opinion. For me to say that a dropped bowling ball will fall downwards would not be considered, by most, to be an "opinion". Thus, there is a big issue whether and when conjecture is an opinion.
- Tastes: Someone's tastes are sometimes referred to as their opinions, but tastes are not opinions. In some ways, tastes are the most factual thing imaginable. "I like lemons" is a fact. It is a more certain fact, in fact, than the sun rising in the east. A taste or preference is simply a statement of someone's mental state. The reason that tastes are sometimes confused with opinions is that most people, when stating a taste, do not explicitly state that it is their taste. Someone who says "The sky is a pretty shade of blue" probably means "I find the color of the sky to be subjectively pleasing to my sense of aesthetics", which is a fact.
- Values: Values are like tastes, but they usually refer to a universal standard. "Littering is wrong" means that something is objectively unpleasant. Of course, any value can be turned into a fact by adding "I think..." to the front of it. "I think littering is wrong" is a fact. Attaching values to be objectively true does refer to facts, although sometimes they are facts that can not be physically tested or proven.
- Classification and Categorization: This is a particularly sneaky way that opinions can be snuck under the radar. For example, "The Beatles are a Pop Band" is a way to classify The Beatles, and to classify them as such is an opinion, or at least leads to opinions. After all "The Beatles are a Pop Band" and "The Beatles are a Rock Band", two reasonable categorizations, both have connotations that reveal the judgment of The Beatles. Likewise, highlighting a certain fact is in itself an opinion. "George W. Bush is from Connecticut" is a fact, but it is also an opinion, since it denotes things that the fact "George W. Bush is from Texas" does not. So is it possible to state a classification for any person or object, without it being an opinion? Is "My Cat is a Mammal" an opinion, because I do not instead say "My Cat is a Eukaryote"
- Appeal to general standards: If I were to say that "Huckleberry Finn is a classic novel", I am stating an opinion that could be divided into a series of facts. Instead of saying "Huckleberry Finn is a classic novel", I could say "Huckleberry Finn is a book that is on the reading lists of over 50% of American Junior and Senior High Schools, and has been continuously in print for over a hundred years, and has a great deal of critical attention paid to it." Besides that would be much longer. Often, an opinion like this is a convenient distillation of a host of facts.
So in the real world, where people seldom deal with mathematical certitude, live is often a mixture of various types of these "opinions". If I say "It looks like it is going to rain, so it is not a good idea to go outside on such a crummy day", I have knitted together three "opinions". "Clouds are casually followed by rain, which I find distasteful enough to categorize the day as 'Crummy'" is one rational supposition that is close to facthood, followed by two factual statements of my own mental state.
In other words, "opinions" can be a great deal of things, and many of them are not that clearly separated from "facts".