Because . . . . . . . . sun was so strong, they decided to sleep during . . . . . . . . day and travel by . . . . . . . . night.

We use the definite article 'the' before nouns that are already known to the reader. The noun 'sun' is already known, hence we use 'the'.
We do not use articles in expressions like 'by day' or 'by night'. Also, we use the article 'the' while referring to a specific 'day' or 'night'.
In the given sentence, 'day' is specific as the sentence narrates a particular day, and 'by night' is an expression that does not use 'the'.