The process you are describing in your question is called transliteration.
The reason for what you see happening in your site, might be because you're using the Transliteration module. Here is a quote from its project page:
Provides one-way string transliteration (romanization) and cleans file names during upload by replacing unwanted characters.
Generally spoken, it takes Unicode text and tries to represent it in US-ASCII characters (universally displayable, unaccented characters) by attempting to transliterate the pronunciation expressed by the text in some other writing system to Roman letters.
Here is a sample of what this module does for "file names":
However, it can also be used to transforms an URL like
mydomain.com/последние-новости-в-Украине-и-мире in something like
mydomain/poslednie-novosti-v-Ukraine-i-mire. To do so, you also need to enable the Pathauto module. After that, go to the Pathauto setting page and check "Transliterate prior to creating alias". For more details on that, refer to "D7 Pathauto transliteration". Attention: this does not "fix" already created aliases (those need to be deleted and recreated).
Note: There is also a transliteration tag on drupal.SE (with only 4 questions using it though ...).