What does 0...0 and 1...1 mean
What exactly does $0...0$ and $1...1$ mean usually?


This simply means a (more or less) long string of $0$s or $1$s or more clearly $000000...000000$ and $111111...111111$.



Related notiational notes, you may have to use soon:

Sometimes the notation $0^n$ and $1^n$ is also used for these strings with exactly $n$ zeroes and ones.

Even more generally it's usually expected that people see the pattern, namely that nothing changes (or else there would be a note about this), for example $\lambda_0,...,\lambda_n$ is expected to be filled with $\lambda_i$ with $i\in \mathbb N_0, 0\leq i\leq n$ or relatedly $(\alpha,...,\alpha)\in \mathbb R^n, \alpha \in \mathbb R$ would be the same principle, that you'd have to fill the blanks with as many $\alpha$s as needed.

One last note: If you'd want to indicate that you want a leading string $0$ and a trailing string $0$ and stuff you don't care about in the middle you'd usually notate it as $n\in\{0,1\}^*$ and $0||n||0$ which means "place an arbitrary string of arbitrary length between the zeroes".