“It was great meeting you the other day.”
You went to a job fair three days ago to look for a job. You met a recruiter for a company and want to continue your communication with her. You write her an e-mail and start by saying this.
It was great meeting you the other day.
This is a polite phrase that you say or write to people you don't know very well, who you meet in a work situation or other formal situation. You usually use this at the end of your conversation with someone, or a few days later when you contact them again. Here are other examples:
It was great talking to you yesterday.
It was great seeing you! Bye!
Note that people also often say "It was great to meet you the other day." The differences between these are pretty small.
The word "meet" can mean two different things - to get together with someone you already know, or to see and speak with someone for the first time. When someone says "It was nice meeting you" or "Great meeting you" it means that they met for the first time.
"The other day" means "a few days ago". You use it to talk about a day that's about 2 to 10 days before today.
So you wouldn't use it if you're talking about something that happened yesterday, and you wouldn't use it for something that happened three weeks ago. You use "the other day" when you don't exactly remember what day something happened, or when it's not important to tell the exact day.
I was talking to somebody about that just the other day.
You can also say "the other night", "the other evening", etc.
"The other day" and "the other night" can be used in business or casual situations.