The problem of deciding whether an input is a palindrome or not has been proved to require $\Omega(\log n)$ space on a Turing machine. However, even storing the input takes space $n$ so doesn't that mean that all Turing machines require space $\Omega(n)$?
Of course, there's no contradiction here, since any function that uses at least linear space also uses at least logarithmic space. But writing $\Omega(\log n)$ does suggest that it's possible for a Turing machine to use less than linear space – after all, why would people spend all that time proving $\Omega(\log n)$ if that was exactly the same thing what seems to be a trivial $\Omega(n)$ bound? So what does it mean for a Turing machine to use less than linear space?