Babu alitaja methali moja huku watoto wakitafuta fasili yake kwenye kamusi.

Alitaja can be broken down as:

• a- = he/she
• -li- = past tense
• -taja = mention / name / state

So alitaja means he mentioned or she mentioned.
In this sentence, because the subject is Babu, it means Grandfather mentioned.

Swahili does not have articles like English the and a/an.
So nouns often appear by themselves:

• Babu = grandfather / the grandfather / Grandfather
• kamusi = dictionary / the dictionary

You understand whether it is a or the from context.

In Swahili, adjectives and numbers usually come after the noun.

So:

• methali moja = one proverb
• watoto wawili = two children
• kitabu kikubwa = a big book

That is normal Swahili word order.

It can do both, depending on context.

• methali by itself can mean a proverb or the proverb
• methali moja explicitly says one proverb
• sometimes moja also has a sense like a certain proverb

In this sentence, one proverb is the most straightforward reading.

Yes, huku can mean here / this side in other contexts.
But in this sentence it has a different function.

Here, huku introduces a simultaneous background action, so it means something like:

• while
• as
• meanwhile

So:

• huku watoto wakitafuta... = while the children were looking for...

This use of huku is very common in narration.

Wakitafuta uses the -ki- form, which often shows an action happening at the same time as another action.

It breaks down like this:

• wa- = they
• -ki- = simultaneous / ongoing in relation to another action
• -tafuta = search / look for

So wakitafuta means something like:

• while they were searching
• as they searched
• in the process of searching

This fits well after huku, which already sets up the idea of a simultaneous action.

Because watoto belongs to the noun class that takes wa- for plural human subjects.

• mtoto = child
• watoto = children

Verbs must agree with their subject, so:

• watoto wanatafuta = the children are searching
• watoto wakitafuta = the children while searching

The wa- shows the verb is referring to children.

Fasili means something like:

• definition
• explanation
• interpretation
• meaning / gloss

In this sentence, it is the meaning or explanation of the proverb.

It is similar to maana, but fasili can sound a bit more formal or more like dictionary-style explanation. That is why it fits nicely with kwenye kamusi (in the dictionary).

Fasili yake means its meaning / its explanation.

Here yake refers to the proverb: the children are looking for the proverb’s meaning.

A useful point: in Swahili, the possessive form agrees with the possessed noun, not with the English-style possessor.

So:

• fasili is a class 9 noun
• class 9 uses ya-
• -ake means his/her/its

So ya + ake = yake

That gives fasili yake = its meaning.

Because Swahili does not separate his, hers, and its the way English does.

The same possessive stem can cover all of these, and context tells you which one is meant.

So yake can mean:

• his
• hers
• its

In this sentence, since it refers to methali (proverb), the natural English translation is its.

Kwenye kamusi means in the dictionary or in a dictionary.

• kwenye is a very common locative form meaning in / on / at
• kamusi = dictionary

So the whole phrase tells you where they were searching for the explanation.

Both can often be translated as in, but kwenye is very common in everyday Swahili and works naturally with places or locations.

So:

• kwenye kamusi = in the dictionary
• katika kamusi is also possible, but may sound a bit more formal depending on context

Here kwenye is perfectly natural.

Yes, a sentence with wakati would also be possible, for example:

• Babu alitaja methali moja wakati watoto walikuwa wakitafuta fasili yake kwenye kamusi.

That would mean roughly the same thing.
But the original version with huku is more compact and flowing, and it sounds very natural in storytelling or written narrative.

So:

• wakati = more explicit when/while
• huku + -ki- form = smoother narrative while/as/meanwhile