In the Diaspora an eighth day of Passover is observed. This day is obligatory by Rabbinical decree and the Sages invested it with all of the sanctity of the Festivals.
All of the laws applicable to the Seventh day (the Festival day required by the Torah) are applicable to the eighth as well.
The second day of the Festival observed in the Diaspora is equivalent to the first, in matters of Halachah, with exceptions made concerning burial, treating the ill, and eggs that were laid on the first day of the Festival.
Nevertheless it is customary in the Diaspora to be somewhat more lenient on this last day of Passover. The leniency that is customary on the eighth day of Passover concerns the relaxation of certain stringencies that people observe on the other days of Passover.
For example, there are many who do not eat matzah that has been soaked in water on Passover, but this stringency is relaxed on the eighth day of Passover observed in the Diaspora.
Similarly, there are many people who observe a stringency on Passover of not eating in someone else's home or of lending or borrowing dishes. This stringency is also relaxed on the final day of Passover observed in the Diaspora.
In the Diaspora, Yizkor, the memorial prayer for the deceased, is said on the eighth rather than on the seventh day of Passover.