In some interviews you might hear that in Israel there are Jewish towns and Arab villages, for example this interview it is used casually. People living in other areas of the world, especially in the west, might think that this is the proof of Apartheid.
It is easy to gloss over the "mixed cities" such as Jerusalem, Haifa, Lod, Ramle, Acre, and of course Tel Aviv that were also mentioned in the same interview. It might be also an "exception proving the rule" that the interviewee (a Muslim Arab woman) lived in Nahariya one of those "Jewish towns".
Elsewhere in the world
Before going in explaining what these terms mean, let me look at a few places around the world.
In Belgium, the heart if Europe, the Flemish and Walloon live in mostly separated places.
Historically there were Hungarian villages in Romania, German, Slav, Croatian etc. villages in Hungary and the same thing was all over Europe. to this day there are villages in some European countries where minorities live and speak their own language.
In many cities in the USA and elsewhere in the world we can see places like Chinatown, Korea-town and Little Italy. We also see separate areas where immigrants from Arab countries live closely together and Jews live in specific areas. It is not universal and 2nd and 3rd generation immigrants started to move out from those areas and started to marry people from other background, but it took a lot of time. This shows that people with similar backgrounds like to live together.
I won't try to judge if the separation or the integration is a better thing, I am just pointing out that the need to live with people with similar background is not unique in Israel.
Historical background
In the early 19th century in the area of today Israel-West Bank-Gaza there were small Arab villages and a few "mixed towns". Eg. In Jerusalem there was a Jewish majority and Arab minority, there was also Jaffa (Israel), Safed/Tzfat (Israel), Tiberias (Israel) and Hebron (West Bank) where there was mixed population.
As pointed out in the article about lie of peaceful co-existence, once in a while there was a pogrom against the Jews in each one of these mixed cities.
In the late 19th century (1881-), in response to pogroms in East Europe (Ukraine, Russia), larger number of Jews started to immigrate to this area that was ruled by the Ottoman Empire. To avoid the pogroms here they bought land and started to set up villages on their own that later grew into towns. For example a place called Rosh Pinna and Zikhron Ya'akov.
Tel Aviv was established later, during the second big wave of immigration.
These waves of immigration are called "Aliyah" from the Hebrew word of "going up to the land of Israel".
Many Jews also moved to the existing cities such Hebron, Jerusalem, and Lod joining the Jews who already lived there.
As the Jewish population of the area grew, the economic opportunities grew as well. Many Arabs immigrated to this are from the areas that are now in neighboring countries such as Lebanon, Syria, Jordan and Egypt. They tended to settle down where other Arabs lived.
This is basically how in modern Israel there are cities we refer to as "Jewish cities" and "Arab villages" and "mixed cities".
Language divide
When thinking about the topic one has to remember that the Jews speak Hebrew and the Arabs speak Arabic. So living together in the same place gives extra challenges. For example we would not want to force the Arab children whose mother tounge is Arabic to learn in a school where the teaching language is Hebrew, would we?
Jewish city - Arab village?
The term "Jewish city" is quite misleading. Some might think it means only Jews can live there. That's not the case at all. It only means it was established by Jews and the vast majority who live there are Jews. This does not mean Arabs cannot live there. There are plenty of Arabs who moved to these "Jewish towns".
The Arabs usually tend to live in smaller places, hence called "villages" or "Arab villages". They usually don't let Jews live there. There are no laws against Jews moving to these villages, but their life would be very difficult.
Mixed cities
As mentioned earlier there are a number of so-called "mixed cities". This basically means that there is substantial percentage of both Jews and Arabs.