A phrasal verb is simply two words that together form a single verb.
As for formality, while it may often be true that phrasal verbs sound a bit more informal than a synonymous verb that is a single word, I don't think that's always the case, for a couple reasons. Sometimes, even in formal settings, the most natural way to say something is by using a phrasal verb. Moreover, some other verbs can be used informally, or as slang, meaning those verbs would sound more informal than a phrasal verb. Therefore, I don't think there's any reason to steer clear of all phrasal verbs in formal writing.
For example, the phrasal verb get up can mean get out of bed after waking up, as in:
I like to get up before 6 o'clock on weekdays, so I can leave the house before rush hour.
If you're trying to avoid get up just because it's a phrasal verb, your available synonyms are slim. One thesaurus I checked offered rise, arise, stir and rouse, but I don't think any of those would be better options, even in a formal document.
A similar example would be make up, which NOAD defines as "be reconciled after a quarrel." The thesaurus offers plenty of examples, but many of them are figurative, or multi-word idioms:
be friends again, bury the hatchet, declare a truce, make peace, forgive and forget, shake hands, reconciled, settle one's differences, mend fences, reconcile
As for an example when a single verb would be more informal than a phrasal one, suppose I told you,
I want to go out driving so I can show off my new car.
I could replace the phrasal verb with the single word floss, but that wouldn't make the sentence more formal. (In fact, it would make the sentence more informal; I could find this definition of floss only in the Urban Dictionary, which specializes in slang.)
I suppose we can often make something sound a little more formal by replacing a phrasal verb with a single verb (for example, I think, "I don't know if I'll ever return to France" may sound a little more formal than, "I don't know if I'll ever go back to France"). Still, that's not always the case; it depends on the verbs in question.
As a footnote, if phrasal verbs were good enough for the eloquent Churchill, they are good enough for me.