The theme is fear, and fear itself. So we have to look at the hallmarks of how fear is constructed in fiction and in real life.
Fear in both mediums is generated through uncertainty; both the actual fear in real life, and how fear is presented within art. I think that the episode tried to present the idea of fear itself in absence of anything else. notice how every time fear was presented in the episode it is heavily cliched; the knocking at the door, the typical creaks which are used in films to create fear within an audience. But we get no clear object to this; the construction of the fear is the end result itself. I think the episode characterises the externalisation of the internal fears of the Dr. Fear's suggested by Clara to be a constant companion to the young Dr, and this is presented I think by framing this remark at the start of the episode with the Dr's musing at being alone. We have seen in prior episodes his isolation from Clara develop, and we've seen through the new series the Dr's isolation from humanity. I've talked about how we saw this in the previous episodes of this series. I see this episode as a continuation of this theme.
With this in mind, I think that the thing underneath the blanket is a question that the text deliberately does not answer. Because, just as fear is constructed to be about uncertainty, the open question left by the text here self referentially presents the very construction of fear the episode creates. So it does not matter what the figure is, because the lack of resolution has a purpose in itself. I think that questioning what it is, then, is meaningless.
Going back to the Dr's fear of being alone, the idea of fear being the Dr's companion starts at the end of the episode, where the Dr is alone in a barn and has his "dream", and fear being described as being his constant companion by Clara. Considering that the Dr is alone, as we've established in previous episodes, his fear is his "constant companion" and shapes who he is. If he always alone, he lives in a state of fear, and his every action is within fear. Therefore his perception of reality is through the lense of his fear, and this shapes the way he relates to the world. His idea about an undetectable creature is merely a metaphor for this aspect of himself.
I think we can link this theme to the idea of the Dr becoming increasingly isolated from Clara. I think this is an episode about the Dr's psychology.
Well, that's my interpretation, for what it's worth.