"Yes, the secretary is inside."
Translation:Igen, a titkárnő bent van.
Sure, a is the definite article in Hungarian - it just means "the," and for the most part you use it any place you'd use "the" in English. There are some differences in when it's used, but you'll get used to those as you go on.
So your sentence Igen, titkarnő bent van was like "Yes, secretary is inside." It sounds wrong in Hungarian for the same reason it's wrong in English.
There are two spellings: a before a consonant, and az before a vowel, so:
the secretary - a titkárnő, but
the apple - az alma