What is the meaning of $\{0, 1\}^{L}$?

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I've searched for this but suspect I don't know what to call it, so of course can't find information on it. I'm reading through a text that includes this:

$$C := \{0,1\}^L$$

I'm not sure what the exponent $L$ indicates here.

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$L$ is the length, the set $\{0,1\}^L$ can be seen as all words consisting of bits of length $L$. (given the crypto-context, not unusual), so it looks like the ciphertext space (the possible values of a ciphertext) are such bit strings.