Sometimes I find people use “day in the life of” instead of “a day in the life of” in YouTube titles. May I ask what is the difference?
The rules for titles are very relaxed compared to the rules for sentences; they do not have to be grammatically correct. Movie and book titles are often noun phrases that indicate the subject of the movie/book. Star Wars is not a sentence, but fills in the interesting part of the sentence "This is a movie about the _______".
"A day in the life of X" is similarly understood to mean "This is a chronicle of an ordinary day in the life of X." (Sometimes it is actually a highly unusual day in the life, in which case the title is meant ironically.)
"Day in the life" is just a shorter version of "A day in the life". Because it is not a complete noun phrase, it is significantly less formal, which as a style choice gives the impression that the video itself is less a work of art and more an unstructured factual retelling, but sometimes it just means the creator was lazy in coming up with a title.