When de is followed by le, they contract to form du.

So les parties “de le” (of the) jour becomes les parties du jour.

Similarly, if de is followed by les, it contracts to des.

However, de la does not contract and remains as is.

In the example you give we do not use de on its own but it has to be followed by the definite article le. So it is le jour and not jour.
Sometimes you will find that partie is not followed by the definite article, but then it has a different meaning.

When partie has the meaning of “game” or designates an activity we do not use the definite article, and thus we have :

La partie de tennis.
La partie de cartes.
Une partie de pêche.

When partie has the meaning of “a part”/ “a portion” of something then we have to use the definite article (le, la or les accordingly) :

Les parties de la maison.
Les parties de l’année.
Les parties des bâtiments réservés à l’usage des¹ copropriétaires.
La partie du² paragraphe soulignée en rouge.

^{1 des ⇒ de les, compulsory elision.
2 du ⇒ de le.}

In parts of the day, “the day” is not a particular day, such as May 30, 2014. It is the concept day — a day in the abstract. A day – any day — has these parts, by definition.

In English we generally do not use a definite article for this. We typically use no article (or sometimes an indefinite article): Man is mortal. In French we generally use a definite article for this: L’homme est mortel.