When describing the mitzva of sefirat ha-omer in Parashat Emor, the Torah addresses both the amount of days and the amount of weeks to be counted. The Torah first describes the counting of seven weeks and subsequently the counting of 50 days until Shavuot. When stating the counting of weeks, however, the Torah adds a qualifier: we should count seven complete - 'temimot' - weeks. Many Rishonim disputed the function of this word 'temimot' and the consequent halakhot which this term dictates.
The most basic application of temimot appears in the derasha of the Torat Kohanim establishing sefira as beginning at night. The actual harvesting of the omer was conducted at night, while the offering of the sacrifice was performed the next day. The counting is assigned to take place at night so that the ultimate counting toward Shavuot will be COMLPETE. Beginning the counting during the day would prevent the process from being 'complete.' This application merely establishes the night of the 16th of Nissan as the commencement of the mitzva of counting. Several Geonim and Rishonim asserted additional halakhot based upon further extensions of the temimot principle.
Perhaps the most renowned application of this term was first stated by the Behag. Tosafot in Megilla (20b), as well as in Menachot (66a), cite the Behag's position that if an entire day were omitted, the ideal form of sefira cannot continue. Since the Torah required temimut, a counting which skipped a day is inadequate. A previous shiur (see shiur #16, 5755, 'Sefirat Ha-omer and the Shita of the Behag') examined the exact nature of the Behag's position. The Shulchan Arukh (Orach Chayim 689) actually cites the Behag's position, and for this reason we are 'machmir' that if an entire day of sefira were omitted we do not continue counting with a berakha. According to the Behag, the word 'temimot' conditions the entire counting and demands that it be complete and uninterrupted.
Several Rishonim (see Ritz Geut in Hilkhot sefirat ha-omer) cite Rav Sadya Gaon as adopting a much more limited expression of the term 'temimot.' Working off the derasha of the Torat Kohanim, Rav Sadya rules that if the first day were not counted, a person cannot continue counting with a berakha, since he has forfeited the temimut quality of the count. In fact, it appears from some records of Rav Sadya's halakha that if one did not count the first night, he may not continue counting for the remainder of sefira – even if he counted during the first day. According to this view, by determining that sefira must begin at night, the Torat Kohanim establishes that to achieve temimut one must begin the counting at night. On the one hand, Rav Sadya Gaon merely applies the underlying logic of the Torat Kohanim. By scheduling the sefira's commencement for the evening due to the requirement of temimut, halakha goes beyond suggesting temimut as an ideal. Temimut is 'me'akeiv,' and in its absence, sefira hasn't been properly conducted. By contrast, the Meiri in Megilla (20b) views the entire concept of temimut as ideal but not binding. Ideally, sefira should begin at night, but if omitted, it may also begin the next day.
The Behag extended Rav Sadya's logic one step further by claiming that the omission of any day would undermine the temimut of the entire counting.
Tosafot dismiss the Behag and Rav Sadya's perspectives and propose a different role for temimut. If a person did not count during the evening, he may not count with a berakha the following day, since the counting will not be considered 'complete.' Just as the Torat Kohanim determined that sefira must begin at night to lend a quality of 'temimut' to the entire 50-day counting process, Tosafot similarly demand that each and every day be counted at night so that each day is a more complete counting. Again, the Shulchan Arukh cites this opinion, and therefore, if one fails to count at night, he omits the berakha when counting the following day. Tosafot thereby effects a major shift in the meaning of temimot. According to the derasha of the Torat Kohanim, and even according to the extension of the Behag, the term modifies the nature of the overall counting. According to Tosafot, however, it determines the nature of each and every day which is counted.
A final view of temimut is iterated in the name of Rav Hai Gaon. Even if we adopt the Behag's notion that the overall counting must be characterized by temimut, merely skipping one night will not necessarily ruin the entire process. After all, the process is divided into two countings: the counting of days and the counting of weeks. As stated earlier the pivotal term 'temimut' only appears when describing the counting of weeks. This approach is clearly outlined by Abaye who claims in Masekhet Menachot, "There is a mitzva to count days and a mitzva to count nights (and both are to be maintained even without a Beit Hamikdash)." (For a more complete analysis of the different countings of sefirat ha-omer, see shiur #13 of this series – 'Sefirat Ha-Omer Without a Beit Hamikdash.') According to Rav Hai Gaon, even if temimut is ruined within the counting of days, it can be recovered at the level of weeks. Even if a person forgot a day, as long as he did not forget a day which concludes a week (7, 14, 21 etc.) he can continue counting. There are actually two versions of Rav Hai Gaon's position: The Ritz Geut cites him as claiming that temimut can be realized EITHER through days or through weeks. The Shibalei Ha-leket, however, cites him as claiming that temimut ONLY applies to the week counting but is not at all relevant to the day counting. Either way, by recovering the count before the current week concludes, a person can maintain temimut. This shita, too, views temimut as a quality which qualifies the overall counting, and as a binding halakha, not merely an ideal.