A one house counter house is a standalone house. It's not inside of or attached to anything else — it's a single-family home, probably with its own yard and driveway and stuff.

一軒家 is an everyday word that refers to a standalone house, as opposed to an apartment or condo. You'll hear it in real estate, casual conversations about housing, or when describing someone's living situation.

This word is a jukugo word, but it uses a mix of on'yomi and kun'yomi readings. 一 and 軒 use the on'yomi you learned with the kanji, so you should be fine there — just watch out for the いち changing to いっ. 家 uses its kun'yomi や reading, which you've seen with words like 空き家 and 家賃. Here's a mnemonic in case you need help with that one:

Ask most people if they want to live in a standalone house, and they'll say "yah (や)." No screaming babies next door, no late-night drum solos from the neighbors — yah, it's kind of a no-brainer.