The Rishonim had a custom to refrain from eating meat and drinking wine during the period of mourning over the destruction of the Temple. Some observed this stringency every weekday throughout the Three Weeks, while others did so only during the week in which Tisha Be-Av fell. Most Rishonim maintain that the proper practice is to refrain from consuming meat and wine during the Nine Days.
According to the Mishna (Ta’anit 26b), the prohibition on eating meat and drinking wine only applies to the se’uda ha-mafseket, the final meal before the fast of Tisha Be-Av begins. Nonetheless, the Rishonim adopted the stringency of refraining from consuming meat and wine during the entirety of the Nine Days, because meat and wine are known to bring joy, and the Sages said, “When Av arrives, we curtail our joy.” Furthermore, when the Holy Temple was destroyed, we ceased bringing meat offerings and pouring wine libations on the altar. Consequently, it would have been proper to abstain entirely from eating meat and drinking wine until the Temple is rebuilt, but we are unable to withstand such a decree (see BB 60b). However, during the periods that were established as times of mourning over the destruction of the Temple, there is room to be stringent.
In practice, the Ashkenazic custom to abstain from meat and wine throughout the Nine Days includes Rosh Ĥodesh Av. This was also Arizal’s practice. According to the custom of most Sephardim, however, one may eat meat and drink wine on Rosh Ĥodesh; the prohibition begins when the day ends (MB 551:58, Kaf Ha-ĥayim 551:125). We are stringent on the tenth of Av as well, taking care to refrain from eating meat and drinking wine then too, because the Temple continued to burn on that day. Ashkenazim abstain only until midday on the tenth of Av, while most Sephardim are stringent until the end of the day on the tenth of Av (SA and Rema 558:1, Kaf Ha-ĥayim, ad loc. 10).
The custom of Yemenite Jews is not to be stringent about this at all; they eat meat and drink wine throughout the Nine Days, only abstaining from meat and wine at the se’uda ha-mafseket, as the Mishna rules.