Capitalization rate is used primarily in the RE industry where it is goes by Cap rate. In equity market unless you are talking about REIT it is discount rate.
It is the rate that represents your minimal acceptable return.
For instance lets say have two projects to work on A and B, A gives your 10% return and B gives your 15% return. Now each of these project has same payback period.
Now if you have decided that you will go with project A because it has higher return, you need money to execute it. Either now you might have your own money to use for this project, which might give you return say 5% if kept in bank or you might take a loan where you might be paying 8%.
So Cap rate or discount rate is the rate that represents best use of that money.
In public equity market use the term discount rate, the person you are referring is running HF in US so it might be okay for him to assume 4% as discount rate.
So if you find that a value for stock is 100 and its price is 70 so it is trading at 30% discount to its intrinsic value so you will buy it and hope that market becomes rational again and realize the true potential for that security and give you a chance to realize that gain.