Since world war II English has a very big influence on German language. Everybody living in Germany and Austria (and I guess also in Switzerland) who is now younger than about 60 years did learn English as a student in School. Many younger people even started learning English in preschool. Also many people are using English every day in their jobs, and we have some radio stations broadcasting only or mainly in English.
So in German spoken countries the knowledge of English is very high, and so a big amount of English words have been included into German language in the last decades. (These words are called anglicisms, there are thousands of them in the German language.)
Some German words are long and bulky, and if there is an English word with the same meaning, that is slim and slips out of the mouth easily, then the chances are high, that it will be used instead the original German word:
Entschuldigung - 4 syllables, 1 clumsy consonant-cluster (»ntsch«)
sorry - 2 syllables, 0 consonant-clusters
So, »sorry« has establish itself as an adequate alternative to »Entschuldigung«.
»Entschuldigung« is just an ellipsis. The full expression would be:
Ich bitte um Entschuldigung - 4 words, 8 syllables, 1 consonant-cluster
Wir bitten um Entschuldigung - 4 words, 8 syllables, 1 consonant-cluster
sorry - 1 word, 2 syllables, 0 consonant-clusters
Another German alternative is:
Es tut mir/uns leid - 4 words, 4 syllables