(Was ist der Unterschied (!) zwischen ...) Steve is correct in that "das Entschuldigen" is a gerund. However, one usually says "Entschuldigen Sie" or "Entschuldigen Sie bitte", which is the imperative form, same es "excuse me". "Entschuldigung" is a short form of "Ich bitte um Ihre Entschuldigung", same as "pardon" for "I beg your pardon". So you will hear both "Entschuldigen Sie" and "Entschuldigung", but never "Entschuldigen" alone.

I believe that "Das Entschuldigen" is an example of a gerund, which is simply adding the neuter article "das" to a verb and then capitalizing it to make the verb act as a noun. "Das Entschuldigen" is the act of excusing, whereas "Die Entschuldigung" is the excuse itself.

entschuldigen is the verbform of Entschuldigung (noun) jemanden entschuldigen = to excuse somebody Ich entschuldige, wir entschuldigen = I excuse, we excuse entschuldigen Sie bitte = Excuse me please Entschuldigung = Sorry, Pardon!, Apology