An inference is an educated guess using deductive and inductive thinking, where you derive the meaning of something out of the information that you are given.
This question seems to be aimed at someone new to the novel. If this is the case, then a good inference would be that the letter is one made red because of something that it represents which may or may not be bad. The letter red asserts that the letter must signify something that means "danger," or "warning." Whoever receives, uses, or identifies with such letter much be in a situation that renders them dangerous or concerned about something. Think about getting a 'red mark.' It is the same thing.
Now let's look at what it really is.
The scarlet letter, as its description says, is such an identification. In this case, it is in the form of a letter. It is red because it denotes that the person wearing it may have done something inappropriate. Since this is Puritan Boston, the color red is often associated with crimes of passion, sins of the blood, and something overall evil.
After reading the novel you will realize that what Hester Prynne did, as the woman condemned to wear the scarlet letter on her chest, was not necessarily evil, but it was considered shocking and completely wrong under the bible-based parameters of her society.
See, Hester Prynne is a Puritan woman who has given birth to a child with someone from the community whose name she refuses to give up.
Her child was born out of wedlock; the father of the child is presumed to be one of the married men of the village, and Hester's husband, while is presumed dead, has not officially been declared so. Therefore, the magistrate of the village, under their old laws based on public humiliation, have accused Hester of adultery and have made her ear a red letter "A," for adulterer, on her chest.
Keep in mind, Hester was mad and hurt and humiliated,but she struck back. Her scarlet letter was made by herself and actually exerted all the qualities and descriptions that would befit an award, and not a token of shame:
On the breast of her gown, in fine red cloth, surrounded with an elaborate embroidery and fantastic flourishes of gold thread, appeared the letter A. It was so artistically done [...] that it had all the effect of a last and fitting decoration to the apparel which she wore, and which was of a splendour...
In other words, Hester "owned" her punishment and saw it fit the way that she wanted it to, gaining some angry enemies along the way for doing so.
Therefore, an inference for this is that the scarlet letter is a red letter meant to be work as a sign of identification for something that someone did, or to describe someone for whatever reason. Now you know exactly what the letter is and the purpose that it was intended to serve.