Learn Finnish: Meidän poimimamme marjat ovat lautasella. - The berries picked by us are on the plate.

It is built from the verb poimia (to pick). You take the strong stem poimi- and add the agent participle ending -ma. Because the sentence specifies who picked the berries using the genitive pronoun meidän (our), you must attach the matching possessive suffix -mme to the end, giving you poimimamme.

Since marjat (berries) is plural, why doesn't the participle poimimamme have a plural marker?

This is a tricky rule with possessive suffixes. When an agent participle modifies a plural nominative noun (like marjat), it normally takes a plural -t ending. However, in Finnish, adding a possessive suffix like -mme overrides and hides that nominative plural -t. If the picker was a specific person without a possessive suffix, you would see the plural: Pekan poimimat marjat (the berries picked by Pekka).

Could I just use a relative clause with jotka instead of this structure?

Yes, you can say Marjat, jotka me poimimme, ovat lautasella. That means the exact same thing and is actually much more common in everyday spoken Finnish. The agent participle structure used here is very elegant and mostly seen in written or formal Finnish.

Why is lautanen (plate) in the adessive case lautasella rather than the inessive case lautasessa?