The list actually contains 24 gods: 12 from Tavastia and 12 from Karelia. This is not a full answer as I'm not an expert in the subject, but roughly translated the list goes as follows.
TAPIO metsästä pyydykset soi
Tapio brought the catch from the forest
Tapio was the king of forests and hunters prayed to him before a hunt.
ja AHTI vedestä kaloja toi
and Ahti brought fish from the water
Ahti is sometimes the god of the sea, but more commonly the name is used for persons in folk stories.
VÄINÄMÖINEN virret takoi
Väinämöinen forged the songs
Väinämöinen is a demigod or a hero who appears in many folk stories. Typically he is described as an old wise man who is skilled in singing spells and plays a kantele. Sometimes he is described as the god of songs and poetry. He was an inspiration for J. R. R. Tolkien's Gandalf.
RAHKO kuun mustaksi jakoi.
Rahko divided the moon black
Rahko is a creature who paints the moon black with tar to cause the moon to wane.
LIEKKIÖ ruohot, juuret ja puut hallitsi ja senkaltaiset muut
Liekkiö ruled grasses, roots and trees and others of that kind
Liekkiö is a spirit similar to a Will-o'-the-wisp. Sometimes a ghost of a child who has been killed.
ILMARINEN rauhan ja ilman teki ja matkamiehet edesvei
Ilmarinen made peace and air and took travelers forward
Ilmarinen is a god or demigod smith. Sometimes he is described as the god of wind, weather and air.
TURSAS antoi voiton sodasta
Tursas gave victory in war
Tursas or Iku-Turso is usually thought of as a sea monster, but sometimes also a god of war.
KRATTI murheen piti tavarasta
Kratti worried of property
Kratti is a screaming ghost that lies above treasure hidden underground.
TONTTU huoneen menon hallitsi, kuin PIRU monta villitsi
Tonttu ruled the ceremony of the room when Piru drove many wild
A Tonttu, or Nisse, is a creature in Nordic folklore. They look somewhat similar to garden gnomes. Nowadays they are mostly associated with Christmas as the helpers of Santa Claus.
Piru is a demon or an evil spirit. The name is also used for Satan.
KAPEET myös heiltä kuun söivät.
The Kaves also ate the moon from them.
Kave ("kapeet" is plural, "kave" is the singular form) is a spirit that is usually thought to restore the moon. According to this list however, they eat the moon.
KALEVANPOJAT niityt ja muut löivät
Sons of Kaleva created the fields and others
The sons of Kaleva are ancient giants who were the early settlers of the land. They left when Christianity spread to their lands. In some earlier sources they seem to be human heroes (Väinämöinen, for example, is sometimes one of them).
RONGOTEUS ruista antoi, PELLONPEKKO ohran kasvun soi. VIRANKANNOS kauran kaitsi, muutoin oltiin kaurasta paitsi. ÄKRÄS herneet, pavut, nauriit loi, kaalit, liinat ja hamput edestoi.
Rongoteus gave rye, Pellonpekko granted the growth of barley. Virankannos tended oat, otherwise [people] were without oat. Äkräs peas, beans, turnips created, cabbages, flax and hemp brought forth
Rongoteus, Pellonpekko, Virankannos and Äkräs are spirits or gods who made different crops grow.
KÖNTYS huhdat ja pellot teki.
Köntys cleared woodlands [for farming] and made fields
Not much is known of Köntys. He/she/it doesn't appear in other sources, at least not with the same name ("köntys" means a clumsy person in modern Finnish). The religious scholar Uno Harva believes he was a creature similar to the sons of Kaleva.
Ja kun kevätkylvö kylvettiin, silloin UKON malja juotiin.
And when the spring plantings were sown, then Ukko's toast was drunk.
Ukko was the god of weather, thunder and harvest. He was the most significant of the gods.
The word "ukko" means "old man". This is believed to be an euphemism to avoid referring to him by his real name. It is thought that Perkele -- which in modern use means Devil -- might have originally been Ukko.
Kun RAUNI Ukon nainen härskyi, jalosti Ukko pohjasta pärskyi. Se siis antoi ilman ja vedentulon.
When Rauni, Ukko's woman sprayed, nobly Ukko from bottom splashed. That then brought air and rain.
This line is a bit cryptic and has different interpretations.
The name "Rauni" doesn't appear in other sources. One interpretation is that Rauni is the wife of Ukko, but it could refer to Ukko himself too. The line could be translated as "the woman of Rauni ukko" (as mentioned above, "ukko" means "old man") rather than "Rauni, Ukko's woman".
The meaning might be that Rauni is a goddes of thunder and the spraying and splashing in the line refers to an argument between her and Ukko creating storms. It is however also speculated that she might be a goddes of fertility and the line is about hieros gamos.
The wife of Ukko is sometimes called Akka, which means "old woman".
KEKRI se lisäsi karjan kasvun
Kekri improved growth of cattle
Kekri usually refers to a celebration held in autumn. Agricola's list is the only source for it meaning a god, and modern researchers believe that Agricola was mistaken.
HIISI metsäläisistä soi voiton
Hiisi granted victory of the people of the forest
Hiisi originally meant a sacred grove or other place of worship, but later came to mean some kind of an evil spirit. The word is often used as a translation for "goblin".
VEDENEMÄ vei kalat verkkoon.
Vedenemä took fish to a net.
Vedenemä, or Veden emo (literally "waters mother"), is a water spirit that fishers asked for luck in fishing.
NYYRIKKI oravat antoi metsästä. HITTAVAINEN toi jänikset pensaasta.
Nyyrikki gave squirrels from the forest. Hittavainen brought rabbits from the bush.
Nyyrikki and Hittavainen are spirits who help hunters.