Frederick C. Copleston and Bertrand Russell were debating the existence of God. The quote comes from the first part of the debate. To put this in broader perspective to understand why Russell is bringing up the term "analytic", let's follow part of the debate.
Copleston starts with an argument from contingency for God's existence claiming that God "cannot not exist". Here is the conclusion:
...since objects or events exist, and since no object of experience contains within itself the reason of its existence, this reason, the totality of objects, must have a reason external to itself. And that reason must be an existent being.
Russell responds by introducing "Necessary Being" and claiming that "necessary" can only be applied to analytic propositions, those which it is self-contradictory to deny:
The word "necessary" I should maintain, can only be applied significantly to propositions. And, in fact, only to such as are analytic -- that is to say -- such as it is self-contradictory to deny. I could only admit a Necessary Being if there were a being whose existence it is self-contradictory to deny. I should like to know whether you would accept Leibniz's division of propositions into truths of reason and truths of fact. The former -- the truths of reason -- being necessary.
Copleston disagrees producing a counterexample, a necessary proposition that is not analytic:
Take the proposition "if there is a contingent being then there is a Necessary Being." I consider that that proposition hypothetically expressed is a necessary proposition. If you are going to call every necessary proposition an analytic proposition, then -- in order to avoid a dispute in terminology -- I would agree to call it analytic, though I don't consider it a tautological proposition. But the proposition is a necessary proposition only on the supposition that there is a contingent being.
Russell then denies the "idea" of a Necessary Being:
The difficulty of this argument is that I don't admit the idea of a Necessary Being and I don't admit that there is any particular meaning in calling other beings "contingent."
Furthermore, he notes:
The word "necessary," it seems to me, is a useless word, except as applied to analytic propositions, not to things.
This may be enough to answer the OP's question about what Russell means by "analytic".
Although Russell is referring to analytic propositions from the semantic distinction between analytic and synthetic propositions, his motivation is to claim that anything that can be usefully called "necessary" must also be an analytic proposition. Copleston disagrees.
Fr. Copleston vs. Bertrand Russell: The Famous 1948 BBC Radio Debate on the Existence of God Retrieved on July 2, 2019 from Evangelical Catholic Apologetics at http://www.biblicalcatholic.com/apologetics/p20.htm