This is the 526th most frequent Russian word.
ко
"Ко" is a preposition in Russian, meaning "to" or "toward," used before certain words for euphonic reasons.
The word 'ко' is used here as a preposition. It means 'to' and is used before the noun 'двери' because the next word starts with the consonant cluster 'дв', which makes 'к двери' harder to pronounce. This is a phonetic adaptation.
Я подошёл ко двери.
I approached the door.
Here, 'ко' is again a preposition, meaning 'to,' and is used instead of 'к' because 'мне' starts with the consonant 'м'.
Он прислушивался ко мне.
He was listening closely to me.
In this sentence, 'ко' is used for euphonic reasons before the noun 'входу' to facilitate smoother pronunciation and is interchangeable with 'к' in more formal texts.