Term for asking a question to create context

Sometimes to start a conversation or to bring up a subject I ask a question. I ask it in hopes that they know the answer, I'm not seeking knowledge or an explanation, but instead I'm looking to create a context for the conversation.

An example question might be something as simple as "Remember yesterday when we talked about [something we talked about yesterday]?" Obviously I don't expect them to just say "yes, I remember" and that's that. I'm bringing that conversation into mind as the context for this conversation. I imagine it's a question and not a command or a statement because 1) they may not actually remember the the conversation from yesterday and 2) courtesy.

Is there a name or phrase for this kind of question?

You can call it a

lead in : something that leads in or introduces; an introduction to a subject

Initially I thought about the expression, breaking the ice; although it's usually used in those embarrassing situations where nobody knows anybody and a deathly silence ensues, a friendly question as an opener can certainly be used as a pretext for a conversation or exchange of information.

It's secondary meaning as defined by The Free Dictionary is:

Break the ice idiom
2. Fig. to initiate social interchanges and conversation; to get something started.
It's hard to break the ice at formal events.

Opener n. A remark used as an excuse to initiate a conversation:
My store of conversational openers seems thoroughly inadequate to the task.
Sitting down beside him, Brenna wracked her brain for a conversation opener.

Conversation opener
A conversation opener is an introduction used to begin a conversation. They are frequently the subject of guides and seminars on how to make friends and/or meet people. Different situations may call for different openers [...]

An opener often takes the form of an open-ended question, which can lead to further comments or conversation as well as creating topics for future conversations (e.g. "How's your mandrill doing?").

A closed-ended question (e.g. "Nice weather today, isn't it?") is regarded as potentially less effective because it can be answered with a simple "Mm-hmm," which is essentially a conversational dead end, requiring the initiater of the conversation to start from scratch.

Consequently, according to Wikipedia, the question "Remember yesterday when we talked about [X]?" would be termed as a close-ended question. As the OP rightly observed when speaking with friends a simple "yes" or "no" response is not expected, but a question is just one of many informal "tactics" that people employ everyday in order to introduce a topic or start a conversation.