Wakati kampeni ilikuwa ikiendelea, meya alikuwa akitembea sokoni na kuwasalimia watu.

Here wakati means when or while. It introduces a time clause:

Wakati kampeni ilikuwa ikiendelea = While the campaign was going on

Literally, wakati can also mean time, but in this sentence it is functioning like a conjunction.

Because kampeni takes class 9 agreement in Swahili. The subject prefix for class 9 is i-, so:

i-li-kuwa

• i- = subject marker for kampeni
• -li- = past tense
• -kuwa = be

So kampeni ilikuwa means the campaign was.

A lot of borrowed nouns like kampeni stay the same in form, but they still control agreement.

This is a very common Swahili way to express an ongoing action in the past.

Breakdown:

• ilikuwa = it was
• ikiendelea = continuing / going on

Together, ilikuwa ikiendelea means it was continuing or more naturally it was going on.

So Swahili often uses:

past form of kuwa + verb with -ki-

to express something like the English past continuous, such as was happening, was walking, was running, and so on.

In this kind of sentence, -ki- helps show an action that is in progress or happening at the same time as something else.

Examples here:

• i-ki-endelea = it continuing
• a-ki-tembea = he/she walking

When these forms come after alikuwa / ilikuwa / walikuwa, they often create a past progressive meaning:

• alikuwa akitembea = he was walking
• ilikuwa ikiendelea = it was going on

In other contexts, -ki- can also mean something like if / when / while, so learners often notice it in several different uses.

Because alikuwa akitembea means was walking, while alitembea usually means walked.

So the difference is:

• alitembea = simple past, a completed action
• alikuwa akitembea = past continuous, an ongoing action

In this sentence, the mayor is being described in the middle of an ongoing situation, so alikuwa akitembea is the more natural choice.

Even though meya is a borrowed word and does not look like a typical class 1 noun, it refers to a single human being. Human singular nouns normally take class 1 agreement, which uses a-.

So:

• meya alikuwa = the mayor was
• plural would be meya walikuwa if you meant the mayors were

This is very common in Swahili: a noun may not visibly show its class, but it still follows normal agreement rules.

Soko means market.
When you add -ni, you get a locative form:

sokoni = at the market / in the market / to the market

In this sentence, sokoni means the mayor was walking in/at the market.

This -ni ending is very common with places:

• nyumbani = at home
• shuleni = at school
• mjini = in town

The wa- is an object marker referring to watu, which is a class 2 noun.

Breakdown:

• ku- = infinitive marker
• wa- = them
• salimia = greet

So kuwasalimia watu literally has the sense of to greet them, the people.

In Swahili, object markers are often used with human objects, especially when they are definite or prominent in the sentence. You can also hear kusalimia watu, but kuwasalimia watu is very natural.

Swahili often links actions efficiently by using na + infinitive after the main verb phrase.

So:

alikuwa akitembea sokoni na kuwasalimia watu

means:

he was walking in the market and greeting people

The tense and general time frame are already established by alikuwa akitembea, so Swahili does not need to repeat a full finite verb for the second action.

A fuller version would be possible, but it would sound heavier and less smooth.

Yes.

• mtu = person
• watu = people

This is one of the most important noun pairs in Swahili. Since watu is class 2 plural, it triggers class 2 agreement, which is why the object marker in kuwasalimia is wa-.

Yes. Swahili can move that clause around without changing the basic meaning.

For example:

• Wakati kampeni ilikuwa ikiendelea, meya alikuwa akitembea sokoni na kuwasalimia watu.
• Meya alikuwa akitembea sokoni na kuwasalimia watu wakati kampeni ilikuwa ikiendelea.

Both are natural. Putting wakati... first gives the time background first, which is often a very natural way to tell the story.