In the first stanza of "The Cold Within," the speaker informs us that six people are "trapped" in a very cold and dark setting. The meeting of these six people is one of coincidence ("happenstance") and each person is holding a stick of wood.

Next, the speaker tells us that the people are sitting around a fire but this fire is on the verge of dying out because it needs extra wood. The first man looks around the group and decides to not put his stick of wood on the fire because there is a black person sitting across from him. In other words, his racism prevents him from adding his stick of wood to the fire: he would rather be cold than help a person from a different race. 

This example of racism sets the tone for the remaining stanzas of the poem. 

If we are talking about the same poem, then the answer is as follows (I am providing a link so you can see what poem I am referring to).

The poem as a whole is about the need for human beings to tolerate one another.  It speaks of how hatred of other people because of their race or religion or some other characteristic ends up hurting all people.

In the first stanza, we are introduced to the basic setting -- there are six people around a fire each with a stick of wood.

The second stanza shows us the first instance of bigotry.  One of the men notices that another of the six is black.  Because he saw a black person, he did not put his log in the fire because he did not want to help a black person.