Siivouspäivänä vien vanhat laatikot varastoon ja pesen lattian.

Siivouspäivänä is siivouspäivä + the essive case ending -nä.

Here it expresses time when something happens, so it means on cleaning day.

A few useful points:

• siivous = cleaning
• päivä = day
• siivouspäivä = cleaning day
• siivouspäivänä = on cleaning day

Finnish often uses the essive this way with days, dates, and occasions:

• maanantaina = on Monday
• jouluna = at Christmas
• syntymäpäivänä = on a birthday / on one’s birthday

So this is a very common time expression pattern.

Because Finnish usually leaves out the subject pronoun when it is clear from the verb ending.

Here:

• vien = I bring / I take
• pesen = I wash

Both verb forms already show first person singular, so minä is not necessary.

You could say:

• Minä vien vanhat laatikot varastoon ja pesen lattian.

But it sounds more natural in many contexts to omit minä, unless you want extra emphasis, such as:

• Minä vien laatikot, en sinä.
  I’ll take the boxes, not you.

They are both present tense, first person singular forms.

• viedä = to take, to bring
  → vien = I take / I bring
• pestä = to wash
  → pesen = I wash

For an English speaker, it helps to remember that the Finnish present tense can cover several meanings that English often separates:

• I take
• I am taking
• I will take (sometimes, depending on context)

So vien and pesen do not necessarily mean only a habitual action. In a sentence like this, they can describe a planned or typical action on cleaning day.

Because vanhat laatikot is a total object in the plural.

In this sentence, the speaker is taking the whole set of old boxes to the storage room, so Finnish uses the nominative plural:

• vanhat laatikot

If the meaning were some old boxes, old boxes in general, or only part of them, Finnish would use the partitive plural:

• vanhoja laatikoita

Compare:

• Vien vanhat laatikot varastoon.
  I’m taking the old boxes / all the old boxes to storage.
• Vien vanhoja laatikoita varastoon.
  I’m taking some old boxes to storage.

So the choice tells you something about whether the object is seen as a complete whole or only a partial/indefinite amount.

Because in Finnish, adjectives usually agree with the noun they describe.

Here:

• laatikot = boxes, nominative plural
• vanhat = old, also nominative plural

So both words must match:

• vanhat laatikot = old boxes

This agreement happens across cases and numbers:

• vanha laatikko = an old box
• vanhan laatikon = of the old box / the old box as certain object form
• vanhassa laatikossa = in the old box
• vanhat laatikot = old boxes
• vanhoissa laatikoissa = in the old boxes

This is one of the most important habits to get used to in Finnish.

Because varastoon is the form that means into the storage room / into storage.

The ending -oon here is an illative ending, which usually expresses movement into something.

So:

• varasto = storage room, storage
• varastoon = into the storage room / into storage

This fits the verb vien, because the boxes are being moved to a destination.

Compare the location cases:

• varastossa = in the storage room
• varastosta = out of the storage room
• varastoon = into the storage room

So:

• Vien laatikot varastoon. = I take the boxes into storage.
• Laatikot ovat varastossa. = The boxes are in storage.
• Tuon laatikot varastosta. = I bring the boxes out of storage.

Because lattian is a total object form.

In an affirmative sentence, a singular total object often looks like the genitive singular:

• lattia = floor
• lattian = the floor, as a total object

So:

• Pesen lattian. = I wash the whole floor.

If you used the partitive:

• Pesen lattiaa.

that would suggest something like:

• I am washing the floor (focusing on the ongoing action), or
• I am washing some floor surface / not necessarily the whole thing

For learners, a useful basic rule is:

• total/completed whole object → often genitive-looking singular or nominative plural
• partial/incomplete/ongoing/indefinite object → partitive

So in this sentence:

• vanhat laatikot = all the old boxes
• lattian = the whole floor

This is a very common learner question.

Historically and grammatically, many grammars describe this as the accusative object, but in practice the form here is identical to the genitive singular:

• lattian

So for beginners, it is often easiest to think:

• in a normal affirmative sentence, a singular total object often looks like the genitive singular

Examples:

• Luen kirjan. = I read the book.
• Syön omenan. = I eat the apple.
• Pesen lattian. = I wash the floor.

More advanced grammar may distinguish between genitive object and accusative, but at an early stage, the important thing is understanding why this object is not partitive.

Yes, Finnish word order is fairly flexible.

The given sentence:

• Siivouspäivänä vien vanhat laatikot varastoon ja pesen lattian.

is very natural. It starts with the time expression siivouspäivänä, which sets the scene: on cleaning day.

But other orders are also possible, depending on emphasis:

• Vien siivouspäivänä vanhat laatikot varastoon ja pesen lattian.
• Pesen lattian ja vien vanhat laatikot varastoon siivouspäivänä.

The original version is probably the most neutral if the speaker wants to begin with when this happens.

Also notice that the second clause does not repeat the subject:

• vien ... ja pesen ...

That is normal, because the same subject I applies to both verbs.

Finnish has no articles like a or the.

So meanings like a box, the box, boxes, or the boxes are usually understood from:

• context
• word order
• object case
• whether the thing is already known or specific

In this sentence:

• vanhat laatikot naturally comes across as the old boxes
• lattian naturally comes across as the floor

That does not mean the forms themselves contain a separate word meaning the. Finnish simply does not mark definiteness the same way English does.

This is why a literal word-for-word translation can be misleading. Finnish often leaves English-style article information to context.