An example of a string of length 10 over the english alphabet: helloworld. An example of a string of length 5 over the integers 0 through 9: 31337. An example of an ASCII string (mix of letters and digits and symbols) of length 8: tommyd#1. We can use other things other than these more common character sets as well. $\heartsuit\spadesuit\heartsuit\diamondsuit$ is a perfectly valid string of length 4 over the set of playing card suits and they give the example of strings specifically only using zeroes and/or ones being given the special name of "bit strings" such as 101101 or 000111 or even 11111. (note that 11111 is a perfectly valid example of a bit string even though no zeroes appeared. All that mattered was that every character that did appear was either a zero or a one)
Now... whether we wrote it as helloworld or if we wrote it as $(h,e,l,l,o,w,o,r,l,d)$ or as $\{(0,h),(1,e),(2,l),(3,l),(4,o),\dots\}$ or some other way, in maths we frequently switch between representations of these types of objects freely. All three of these are different ways of writing the string helloworld down. It can be useful to think of it as a function, it can be useful to think of it as a tuple, but it is shortest and easiest to write simply as the letters themselves without commas or parentheses etc... as it takes the least time and effort to write it that way.
As for the null string, also called the empty string, it is exactly as it sounds. It is the length zero string, the string with no characters appearing in it. If you think of the words appearing on a page in a book as a string, the empty string is simply the string corresponding to a blank page.
We can even begin listing the possible strings for a given set. The list of possible bit strings can start: , 0, 1, 00, 01, 10, 11, 000, 001, 010, 011, $\dots$. There are of course infinitely many overall, but there are $k^n$ strings of length $n$ using a character-set of size $k$.
