Subjectivism is basically thinking that something is right because of your own feelings about it. Lewis goes on to talk about how there is no reason for anyone to ever think that they are right without logical proof. He gives the example of a King who rules over all the land. His logic becomes subjective because of his power even though there is no reason for supposing that his logic is truth.
Subjectivism happens because of feelings, traditions, conditions, and attitudes. I especially like Lewis' propositions on subjectivism. These are first, that "the human mind has no more power of inventing a new value than of planting a new sun in the sky or a new primary color in the spectrum." Second, "every attempt to do so consists in arbitrarily selecting some one maxim of traditional morality, isolating it from the rest, and erecting it into an unum necessarium." I believe that these proposals mean that we humans cannot come up with any new ideas because they have all been proposed already. To come up with something new would be to take an old idea and make it appear more important than the rest.
The danger of subjectivism can still be seen today. For example, in my own life, it is easy to think that my own ideas are better than someone else's just because of my traditions and the way that I was brought up. People are generally culturally unacceptive today. This is because they think that their own culture is better than everyone else's. God tells us in scriptures to be humble. This means rising above subjectivism and putting others before yourself.