Conversation schools (called eikaiwa) are companies that offer English classes where students can brush up on grammar they learned the 6 years they studied in junior and senior high, or where students can pick up some additional fundamentals of conversational English, perhaps for traveling abroad, living abroad, dealing with foreigners in Japan, etc.
Many students treat eikaiwa not as a school, but as a gathering place to socialize and meet friends, perhaps gawk at a foreigner, etc. Going once a week like most do, they will really not improve their English unless they are very dedicated, and I don't think you can find that many.
Eikaiwa are a business, and the goal is putting butts in seats and keeping them there. It is often nicknamed "edutainment".