You tend to find formal language in academic journals or official documents and notices where it brings an extra degree of seriousness to the subject. As a general rule, it isn't appropriate for everyday situations.
Here are some examples of formal words with their equivalents in standard English—notice that the formal words are often longer than the standard terms.
It can be tempting to use formal vocabulary in the hope that it will add more weight to what you are saying, or just sound more impressive or sophisticated. You should generally try to resist this temptation. If you use formal English in everyday situations, you can make your writing sound pompous or pretentious. You may also make what you've written sound unintentionally funny, as some writers deliberately choose formal vocabulary to create a comic effect.
Take a look at these two versions of the same information:
Passengers were stranded without comestibles and beverages for hours.
Passengers were stranded without food and drink for hours.
There's nothing ‘incorrect’ with the first sentence, but the use of the formal terms comestibles and beverages is somewhat distracting: the words get in the way of what the sentence is actually saying. The standard English terms in the second sentence have much more impact.
Remember that a long word is not necessarily better than a short one—it's just longer!