Haha...I post the question on italki.com and got comments. I think this sentence is kind of business English. Check the answer as below:
Answer No.1: Let's set up regular 1:1 meetings isn't a standard use but if someone wrote that to me I would take it to mean, the person wants to meet on regular schedule with me one to one. As in we are the only two people who will be in the meeting.
Answer No.2: 1:1 in this case means "one on one". Your manager is asking to setup a regular meeting between the two of you, as the other poster said.
The sentence is not quite clear, however, and would be better written as "Let's setup -a- regular 1:1" or "Let's setup regular 1:1s"
The first sentence meaning "Let's setup a standing/recurring one on one meeting" and the second sentence meaning "Let's setup regular one on one meetings". Essentially the same meaning, but one way you are able to write singular and the other must be plural. You manager did neither.