Post kiam ni purigis la kuirejon, ŝi ridetis kaj diris, ke mi preparis pli bonan tagmanĝon ol ŝi.

Post kiam means after, but literally it is after when.

• post = after
• kiam = when

Esperanto often uses this two-word pattern before a full clause:

• Post kiam ni purigis la kuirejon... = After we cleaned the kitchen...

If you only had a noun, you could use just post:

• post la tagmanĝo = after lunch

But because this sentence has a whole clause, post kiam is the natural choice.

Yes. Purigi comes from:

• pura = clean
• -ig- = to make something become

So purigi literally means to make clean, and in normal English that is simply to clean.

So:

• ni purigis la kuirejon = we cleaned the kitchen

This is very common in Esperanto. Many verbs are built this way from adjectives:

• varma = warm → varmigi = to warm, to make warm
• pura = clean → purigi = to clean, to make clean

Because it is the direct object of purigis.

In Esperanto, the direct object usually takes the accusative ending -n.

• la kuirejo = the kitchen
• la kuirejon = the kitchen, as the thing being cleaned

So in ni purigis la kuirejon, the thing receiving the action is la kuirejon.

This is one of the most important grammar rules in Esperanto.

Ridetis means smiled.

It comes from:

• ridi = to laugh
• -et- = a small or slight version of something

So rideti is like to laugh a little, which in normal English is usually to smile.

Then -is makes it past tense:

• rideti = to smile
• ridetis = smiled

So ŝi ridetis kaj diris means she smiled and said.

Ke introduces a subordinate clause, very often the equivalent of English that.

So:

• ŝi diris, ke... = she said that...

In this sentence:

• ŝi ridetis kaj diris, ke mi preparis...
• she smiled and said that I had prepared / I prepared...

Esperanto uses ke very regularly, often more regularly than English uses that.

Because Esperanto does not follow English-style sequence of tenses in the same way.

In Esperanto, the tense usually shows the actual time of the action, not just its relation to the previous verb.

Here:

• ŝi diris = she said
• mi preparis = I prepared / I had prepared

Since the preparing happened before the saying, English often prefers had prepared. But Esperanto can still use simple past preparis if the time relation is already clear from context.

So ke mi preparis... is perfectly normal Esperanto.

If someone wanted to be extra explicit about an earlier action, they might use a more complex form, but in ordinary Esperanto the simple past is very common here.

This part means a better lunch.

Breakdown:

• pli = more
• bona = good
• pli bona = better
• tagmanĝo = lunch

Because tagmanĝon is the direct object of preparis, it takes -n. The adjective must agree with the noun, so it also takes -n:

• bona tagmanĝo = a good lunch
• bonan tagmanĝon = a good lunch, as a direct object
• pli bonan tagmanĝon = a better lunch, as a direct object

So:

• mi preparis pli bonan tagmanĝon = I prepared a better lunch

Because ol ŝi means than she did, with an omitted verb understood.

The full idea is:

• mi preparis pli bonan tagmanĝon ol ŝi [preparis]
• I prepared a better lunch than she [prepared]

Here ŝi is the subject of the understood verb preparis, so it stays in the subject form ŝi, not the object form ŝin.

This is an important point. After ol, Esperanto often leaves part of the comparison unstated, but you still understand the missing words from context.

So this sentence does not mean better lunch than her. It means better lunch than she prepared.

The commas mark subordinate clauses and help show the structure.

• Post kiam ni purigis la kuirejon, ...
• ... diris, ke mi preparis...

So the commas separate:

1. the introductory time clause: Post kiam ni purigis la kuirejon
2. the ke-clause after diris

Esperanto punctuation is generally fairly straightforward, and commas before clauses introduced by words like ke are very common.

The word order here is the most natural and neutral one, but Esperanto word order is fairly flexible.

Because Esperanto marks the direct object with -n, you can sometimes move words around more freely than in English without losing the basic meaning.

Still, this version is the clearest and most ordinary:

• Post kiam ni purigis la kuirejon, ŝi ridetis kaj diris, ke mi preparis pli bonan tagmanĝon ol ŝi.

You could change the order for emphasis, but a learner should usually stick with this normal pattern:

• time clause first
• main clause next
• reported clause after ke

Tagmanĝo specifically means lunch.

It is built from:

• tago = day
• manĝo = meal

So literally it is something like day-meal, but the normal meaning is lunch.

Related words include:

• matenmanĝo = breakfast
• tagmanĝo = lunch
• vespermanĝo = dinner / evening meal

So in this sentence, pli bonan tagmanĝon clearly means a better lunch.