What does the eighth samurai crest / symbol in this picture signify?

It is the crest (mon) of the Sakai clan. The mon was used to identify a family and was worn on the clothing or on containers or buildings, or wherever a family designation was needed. The linked Wikipedia article goes into more detail. The use of mon became common during the sengoku period in Japan. A brief genealogy of the Sakai clan.

The Sakai were direct retainers of the ruling Tokugawa clan and originally it was suggested that they adopt that clan's hollyhock crest. They chose instead to adopt the yellow sorrel crest, which is similar in appearance to the hollyhock.

The Yellow Sorrel crest of the Sakai clan (left) besides the Hollyhock crest of the Tokugawa (right), who were the lords of the Sakai.

These devices are calls Mons in Japanese languages and they are essential elements of Japanese heraldry. Mons are Japanese arms used to decorate and identify an individual or family. Since a Mon is hereditary, it is equal with a arms in concept but not in principles. Personally, I think Japanese heraldry has some similarities to Polish heraldry, because of a lot of common Mons and arms among clans in each of them.

Heraldic concept is the hereditary feature of a specific device, the factor what is common between Japanese heraldry and European heraldry. Fundamentally, a heraldic system is based upon hereditary transmission of emblems.

Heraldic principles are not necessarily common between Japanese heraldry and European heraldry. For example, in European heraldry we have blazon but in Japanese heraldry there is no such a thing like that.

Many of Japanese Mons are canting arms.

Anyway, the listed Mons, as far as I know, are:

1. ?

2. Qīyào (七曜).

3. Watanabe boshi (渡辺星).

4. ?

5. Hidarimitsutomoe (左三つ巴). Utsunomiya clan, Kobayakawa clan, Saionji family.

6. Marunimitsugashiwa mon (丸に三柏紋).

7. ?

8. Cù jiāng cǎo (酢漿草). Sakai clan, Chōsokabe clan.

9. ?

10. Xìchuān jiǔyào (細川九曜).

11. Sumidateyotsume (隅立て四つ目).

12. Maru ni Taka-Wa (丸に違鷹羽). Some temples assumed the Mon (like Higo).

13. ?

14. Jú (橘). Tachibana clan.

15. ?

16. Nánbù hè (南部鶴): Crane. Nanbu clan.

17. Tsuta (蔦). Tōdō clan.

18. Umebachi (梅鉢): Blossom of plum. Sugawara Clan

19. ?

20. Genjiguruma (源氏車).

There is a good work on Japanese heraldry in English that I strongly recommend it to you:

Dower, John W., The Elements of Japanese Design: A Handbook of Family Crests, Heraldry & Symbolism, 1971.

That crest is called a marunikatabami (丸に片喰 or 丸に酢漿草). The design is an encircled creeping woodsorrel flower. As such it is considered a variation of the more primary, and popular, katabami (片喰) crest, which is the same minus the circular border.

The creeping woodsorrel grows extremely well as a wild weed; it is known for being difficult to uproot once it starts growing. The katabami style crests originated from taking this property as a symbol for "propagating the family with many offsprings". Medieval Japan (and today too) had a very strong belief in continuing the family line; thus, it is easy to imagine why this became a popular design of crests. Later on, the three leaves of the katabami have also been interpreted as symbolising mercy, wisdom and virtue.

Because there was no limitations on how a clan chose their crests, the popular ones are shared by a great number of different families. Sometimes this happens when several clans descended from the same lineage; but often it is the result of nothing more than people picking the same design. This led to variations of the base design being adopted; both by clans wishing to make theirs more unique, as well as by individual members or branches of the same clan, in order to mark internal differences.

Apart from the marunikatabami, other variations exist for the katabami crest. This includes thekenkatabami (剣片喰), which adds "leaves" to the flower indicating swords for a more military flavour, and the nanatsukatabami (七つ片喰), famously used by the Chōsokabe clans. Collectively the Katabami style crests are one of the five main crests of feudal Japan.

From left to right:

• the plain katabami crest: used by clans including the Nitta, the Hida, the Nakajō, the Taga, the Aki Fukuhara, the Sakai, the Shinshi, the Odachi, the Wada, the Kido, the Nakazawa, the Okada, and the Hosokawa Reizei.
• the sword ken katabami crest:, used by clans including the Ukita, the Mimura, the Toshima, the Yamada, the Utanokami Sakai, the Yaku, and the Kayama.
• the circled maru ni katabami crest: used by clans including the Naruse, the Hirose, the Adachi, the Itabe Okano, the Chimura, the Irie, the Tōdo, and the Morikawa
• the circled sword maru ni ken katabami crest: used by clans including the Nakamura, the Hirano, the Shibuya
• the seven flowered nanatsu katabami crest: used by the Chōsokabe clan.