Trzeciego grudnia jedziemy do dziadków na kolację.

In Polish, dates are usually expressed with:

• an ordinal number for the day
• the month name in the genitive

So trzeciego grudnia means on the third of December.

This is a normal date pattern in Polish:

• pierwszego maja — on the first of May
• dwudziestego lipca — on the twentieth of July

English uses on here, but Polish usually does not need a preposition.

Both are in the genitive.

• trzeciego is the genitive form of trzeci (third)
• grudnia is the genitive form of grudzień (December)

This is simply how Polish normally forms dates in sentences like this.

Yes, you can think of an implied word like dnia (day), although native speakers normally just say trzeciego grudnia.

So learners often understand it as something like:

• trzeciego dnia grudnia — literally of the third day of December

You do not normally need to say the extra word; trzeciego grudnia is the standard natural form.

Polish often uses the present tense to talk about a planned future action, especially when the time is already given.

So:

• Trzeciego grudnia jedziemy... = On the third of December we’re going...

This works much like English:

• We’re going to our grandparents’ on December third.

The date makes it clear that the action is future.

Because jechać / jeździć is used for going by vehicle or some form of transport, while iść / chodzić is used for going on foot.

So:

• jedziemy = we’re going / traveling by car, bus, train, etc.
• idziemy = we’re going on foot

This sentence suggests they are traveling to their grandparents’, not walking there.

Yes, pojedziemy is possible, but it feels a bit different.

• jedziemy often sounds like a planned arrangement: we’re going
• pojedziemy is more clearly future perfective: we will go

So both can work, but:

• Trzeciego grudnia jedziemy do dziadków... sounds very natural for a fixed plan.
• Trzeciego grudnia pojedziemy do dziadków... also works, but is a bit more like stating a future action straightforwardly.

Because Polish usually drops subject pronouns when they are already clear from the verb ending.

• jedziemy already means we are going

So:

• Jedziemy do dziadków = We are going to our grandparents’

You can add my for emphasis, but it is not necessary:

• My jedziemy do dziadków = We are the ones going to our grandparents’

It means to the grandparents’ or to the grandparents’ house/place.

In Polish, do + genitive is often used for movement to someone’s home:

• idę do mamy — I’m going to my mum’s
• jedziemy do dziadków — we’re going to our grandparents’

So it does not just mean toward the grandparents as people in an abstract sense; it normally means going to where they live.

Because the preposition do requires the genitive case.

The base form is:

• dziadkowie — grandparents

After do, it changes to:

• do dziadków — to the grandparents’ / to the grandparents

So dziadków is the genitive plural form.

It means for dinner / for supper.

The pattern na + accusative is often used in Polish to show the purpose of going somewhere, especially with meals and events:

• na obiad — for lunch/dinner
• na kolację — for dinner/supper
• na kawę — for coffee
• na imprezę — to a party

So jedziemy do dziadków na kolację means they are going there in order to have dinner/supper.

Because after na in this meaning, Polish uses the accusative case.

• kolacja = nominative
• kolację = accusative

So:

• na kolację = for dinner / for supper

This is very common with destinations, events, and purposes.

Usually it means the evening meal. In English, that may be translated as either dinner or supper, depending on the variety of English and the speaker’s habits.

So both translations can be right:

• We’re going to our grandparents’ for dinner
• We’re going to our grandparents’ for supper

The Polish word itself just tells you it is the evening meal.