Mayai yapo jikoni; nitayakaanga jioni.

Because mayai belongs to noun class 6, and class 6 uses ya- for agreement.

• yai = egg (singular, class 5)
• mayai = eggs (plural, class 6)

So:

• ya-po = they are / they are there for a class 6 noun
• ni-ta-ya-kaanga = I will fry them, where ya- means them referring to mayai

In Swahili, verbs have to agree with the noun class of the subject or object, not just with singular/plural in the English sense.

Yapo is a locative form meaning something like are there / are present / are located.

It breaks down like this:

• ya- = subject agreement for mayai
• -po = a locative element meaning there / at that place

So Mayai yapo jikoni means The eggs are in the kitchen.

A very literal way to think of it is:

• mayai = eggs
• yapo = are located
• jikoni = in the kitchen

Jikoni means in the kitchen or simply the kitchen, depending on context.

The ending -ni is a very common locative suffix in Swahili. It often means in, at, or to a place.

So a learner can often think of -ni as adding a location idea:

• nyumba = house
• nyumbani = at home / in the house

With jikoni, the whole word functions as a place expression: in the kitchen.

It is made of several pieces:

• ni- = I
• -ta- = future tense
• -ya- = them (for mayai, class 6)
• -kaanga- = fry
• -a = final vowel of the verb

So:

ni-ta-ya-kaanga = I will fry them

This is a very common Swahili pattern:
subject marker + tense marker + object marker + verb root

Because Swahili often puts object pronouns inside the verb.

In English, you say:

• I will fry them

In Swahili, that them is often an object marker attached to the verb:

• nitayakaanga

This is especially natural when the thing has already been mentioned. Since mayai appears in the first clause, the second clause can just use the object marker ya- to mean them.

Yes. You could say:

• Nitakaanga mayai jioni = I will fry the eggs in the evening

That repeats mayai instead of using the object marker.

Using nitayakaanga is smoother when the eggs are already known from the previous clause. It is similar to English using them instead of repeating the eggs.

Jioni means in the evening / this evening / evening, depending on context.

Swahili often uses time words without a preposition where English would use in, at, or on.

So:

• jioni = in the evening
• asubuhi = in the morning
• leo = today
• kesho = tomorrow

That is completely normal in Swahili.

The singular is yai.

So:

• yai = egg
• mayai = eggs

This is a useful pair to memorize because it is common and a bit irregular-looking to English speakers.

Often, yes. Many learners encounter both kinds of locative forms.

Very roughly:

• yako can sound more general: are there / are located
• yapo can sound more specifically at that place / present there

In real usage, speakers may choose either depending on style, region, and nuance. For a learner, the important thing is that yapo in this sentence is perfectly correct and natural.

A few useful pronunciation points:

• Swahili vowels are usually pronounced clearly and separately.
• Stress is usually on the second-to-last syllable.

So:

• mayai ≈ ma-YA-i
• nitayakaanga ≈ ni-ta-ya-KAA-nga
• jioni ≈ ji-O-ni

Also, the double aa in kaanga is pronounced a bit longer than a single a.