The Torah commands that we count the fifty days from the holiday of Pesaḥ until Shavuot (see Sefer Vayikra 23:15-16), a tradition that is kept to this day, even though the associated sacrifices can no longer be brought. The first of those pesukim discusses counting seven weeks, while the second discusses counting 50 days. Abaye concludes that there is a distinct commandment to count the days as well as a second commandment to count the weeks.
The Gemara relates that the Sages of Rav Ashi’s study hall counted both days and weeks, while Ameimar only counted days without counting weeks. He explained that after the destruction of the Temple counting was merely zekher le-Mikdash – in memory of the Temple practice – so a partial counting was sufficient.
With regard to the basic requirement to count both days and weeks, the Rambam suggests that nevertheless there is still just a single mitzva of counting, although Rabbeinu Yeruḥam argues that they are two separate mitzvot so that when the Temple stood two separate blessings were made on their performance. It appears that the basic requirement is to summarize the conclusion of each seven days with the words “…that are a single week in the omer,” or “…that are two weeks in the omer,” and so forth. Nevertheless it is common practice today to include both the number of weeks and days in every counting after the first seven days are completed.
Tosafot bring the opinion of the Ba’al Halakhot Gedolot who ruled that someone who missed a day of counting can no longer count, and questioned why this should be true. The Rosh explains that since counting every day is a mitzva there is no reason to think that missing one day should preclude fulfilling the commandment of counting on the rest of the days. Some answer that according to the Behag the mitzva is the full counting, and the daily blessing is on the partial fulfillment of the commandment. In fact, the accepted halakha is that if someone misses a single day he should continue counting, although he no longer can recite a blessing on the remaining days.