• Inuit Uukturausingit (IUR) or Inuit Sign Language is presently attested in parts of Nunavut but may have been spread out over a much larger area historically, hence the "IUR?".
• Ussersuataarneq or Greenlandic Sign Language has an unclear relationship to Inuit Sign Language: it might be related or it might just be descended from Danish Sign Language.
• Hand Talk refers to Plains Indian Sign Language (PISL), with Plains Sign Talk, Great Basin SL, SW Hand Talk, Chumash SL, and Coast Salish SL referring to regional variants of PISL. The area marked "?" corresponds to much of the area covered by PISL in the previous version of Wikipedia's map. I guess they're less certain about the language's extent now?
• PSL refers to Plateau Sign Language, another Indigenous regional lingua franca which was in the east displaced by PISL and in the west displaced by the oral language Chinook Jargon.
• OSL refers to Oneida Sign Language, a modern revival language blending PISL and ASL with influence from Oneida.
• MSL refers to Maritime Sign Language, an endangered settler sign language descended from British Sign Language.
• LSC is Cuban Sign Language.
• OCSL is Old Cayman Sign Language.
• Provisle is also known as Providence Island Sign Language, which may be related to OCSL.
• Konchri Sain is also known as Jamaican Country Sign Language.
• Meemul Chʼaabʼal / Meemul Tziij is Mayan Sign Language.

As for the numbered languages in the corner:

1. ISN = Nicaraguan Sign Language. This is a pretty famous sign language due to the circumstances in which it emerged, basically a bunch of schoolkids developed the language amongst themselves.
2. LESHO = Honduran Sign Language.
3. Lensegua = Guatemalan Sign Language.
4. Didxa ná’ = Albarradas Sign Language. Indigenous village sign language of some Zapotec communities in Mexico.
5. Cha'ya' = San Juan Quiahije Chatino Sign Language. Indigenous village sign language of some Chatino communities in Mexico.
6. LSOR = Orocovis Sign Language. Village sign language of some Afro-Caribbean families in Orocovis, Puerto Rico.
7. Old Boricua SL… I don't know what this is referring to. Puerto Rican Sign Language is descended from ASL so it would be excluded from this map, so it can't be referring to that. The only other mentions of "Old Boricua Sign Language" I can find online are the Wikipedia talk page for this map and some Instagram post sharing this map uncritically. That doesn't necessarily mean that this isn't a real language; if it isn't a real language, I don't know how it got on this map.
8. Keresign = Keresan Sign Language. Indigenous village sign language of the Keres people, Four Corners region.
9. Diné Family SL = Navajo Family Sign. Indigenous village sign of the Navajo people, Four Corners region.
10. Chumash SL: see PISL.
11. Sawmill SL. I don't know why it's placed exactly there on the map, but sawmill workers have historically used signs to communicate over loud machinery.
12. Coast Salish SL: see PISL.
13. MVSL = Martha's Vineyard Sign Language. This was a colonial village sign best known for being one of the main substrates of modern American Sign Language. It was itself likely strongly influenced by the undocumented Eastern Woodlands Algonquian sign language, hence what I said earlier about "ghosts" of Indigenous sign language in ASL.
14. Henniker Sign Language. Another colonial village sign that served as a major substrate for ASL.
15. Sandy River Valley Sign Language. The third colonial village sign that served as a major substrate for ASL.