Breakdown of Deine Entschuldigung ist kein Problem.
sein
to be
kein
no, not any
das Problem
the problem
dein
your (informal)
Questions & Answers about Deine Entschuldigung ist kein Problem.
Why do we use kein here instead of nicht?
Why is it Deine and not Dein?
The word for "your" changes based on the gender of the noun that follows it. Entschuldigung is a feminine noun, which you can easily remember because all German nouns ending in -ung are feminine. Because it is a feminine noun, we must add the -e ending, making it Deine.
Why is it kein Problem without an extra ending like keine?
Problem is a neuter noun (das Problem). Because it is used here to state what something is (the nominative case), the word kein gets no extra ending for neuter nouns.
I usually hear Entschuldigung used to mean "Excuse me". How does it mean "apology" here?
Entschuldigung is actually a capitalized noun that literally translates to "apology" or "excuse". When you say it on the street to get someone's attention or to say sorry, you are essentially just shouting the noun "Apology!" on its own. In this sentence, you get to see it acting as a normal noun.