What you write or make for your local audience may not make much sense to people outside your country. For example, an application made specifically for Chinese locals will be difficult for people to understand in Ukraine. Even if the app’s language is translated into their native language, most terms and terminology may go over their heads. Therefore, localization of the application is a must, which puts the content in accordance with and in context with the audience outside their country.
It basically refers to the adaption of things to suit the people of the country or region so that everything makes sense to them. So, in simple terms, in the example mentioned above, a Chinese saying in the application that reads, “A fool judges people by the presents they give him,” may not be understood by the local people in India since it is foreign to them, so to localize the saying to bring it in context, the process would include finding an alternative to the Chinese saying that people in India won’t find hard to comprehend.
Written material may need to be localized, but the localization process is mainly for cultural adaptation of software, websites, videos, and even video games. It could also refer to other multimedia content, like voiceover and movie dubbing, to adapt to the cultures of different regions, even within a country where the same languages are spoken but with different dialects, norms, and cultures.

Localization is a part of Globalization, which also includes Internationalization. Internationalization actually takes place before localization and includes the overall planning and preparation of the design to harmonize with its audience worldwide. In this process, it is necessary to remove all cultural assumptions and region-specific content so that users can adapt no matter which part of the world they live in.
Localization is the next step after Internationalization is taken care of. This is where the product, be it a website, software or application, is made specific for the intended market. A website made in the US can be internationalized for the world to visit, but it can get even more specific by being localized for people living in France. Apart from translating the website, it can be optimized to have a design that goes well with the French, having contextual reference to their cultures and being relatable to them.
The processes taken before Localization, that is, Globalization and internationalization, are necessary because they make the process of localization easier and minimize the efforts put into localization. If the software is made for a specific country like China, and now it wants to expand to the US, it may contain images and references that people in the US may find offensive. But if the same software had been globalized, it would be neutral and without any reference to any particular country, religion, or culture, and it would take minimum effort to localize it for any specific market.
This is exactly why companies need to consider the business they want to conduct beforehand and plan ahead without being specific about any region or culture. If this process is not taken care of before the business is set up or after a website has been put online with depth, it becomes harder and costlier to localize it for other markets.
Now that the process of localization has been explained in as simple words as possible, you may want to consider getting your product localized by a professional service to cater to a wider and larger audience rather than being limited to local areas.