Yom Rishon L'Shabbat

Yom rishon l'Shabbat" (First day towards the Shabbat) This is referring to the first day of the week (Sunday) which is the first day towards the Shabbat, Monday is the second day towards the Shabbat, Tuesday is the third day towards the Shabbat, etc.  From the beginning of the week we have already established relationship with the Shabbat.

In Shemot (20:8) the Torah says: "Remember the Shabbat to keep it holy." Based on this, our Sages teach that we are obligated to count the days of the week leading up to Shabbat and that the verse teaches that we should remember Shabbat every day of the week. This is to assure that we not forget Shabbat, nor confuse it with another day, in order  to remember daily the creation of the world and its Creator.
Judaism's method of counting the days of the week differs from a non-Jew's method of counting the days of the week.  Non-Jews use names for each day of the week, such as Sunday, Monday, etc. In Judaism, we count the days of the week with an eye towards Shabbat, i.e. Yom rishon l'Shabbat or Shir shel yom - "Today is the first day in (the count towards) Shabbat."