This is something called ʾiʿrāb which is the way of inflecting nouns for case and definiteness. It is only present in MSA, not the dialects, and it's not usually written, because none of the diacritics are usually written ‾\_(ツ)_/‾. The -t- is what the tāʼ marbūṭah (ة) turns into when it's not at the end of a word; the vowel that follows is the case ending; and the -n signifies that it's indefinite (that's called nunation or tanwīn). The course is kind of inconsistent in applying them, but I think it's a good idea to get used to hearing them, even though I personally don't feel like it's that important to be able to produce them yourself.
So the breakdown for حَديقَةٌ ḥadīqatun would be ḥadīq "garden"+-at feminine marker+-u nominative case+-n indefinite.