A mentor of mine is connected with a well known investor that I'm interested in working with and I want to get a warm introduction established through Linkedin introductions. What will the investor be looking for from the introduction to a seed stage company?
Just because two people are connected to each other on LinkedIn, doesn't mean that these two people have a strong connection to one another.
So first, ask your Mentor directly whether (s)he knows this person well enough to make an introduction. Also, I'd suggest that instead of asking that the introduction be made via LinkedIn, that the introduction be made directly via email.
The way this best happens is to email your mentor with a two paragraph email explaining why it is that you want an introduction to this person and explaining why you think this person would want to meet with you.
Then your mentor can forward this email directly to this person with a request for an introduction. If the person replies to your mentor, your mentor will then connect you two directly.
If the investor is interested enough to accept an intro, then you'll likely get a 30 minute to 1 hour in-person meeting or call scheduled.
In terms of what that investor will be looking for, I've written a lot of answers to questions around seed-stage financing that I encourage you to review. I'm happy to schedule a quick call to give you some specific feedback on where you're at and how investors might perceive your progress to date.
Best of luck with this connection!