What are the k-collections described in ch. 8 of "An Introduction to the Analysis of Algorithms" by Sedgewick
I cannot figure out why you were "pretty sure" you were wrong, because you have given a correct example, "a 3-collection from Table 8.1 is 2213, where the last letter (number 3) occurring just at the end".

Here are 2-collections.
1112, 1113, 2221, 2223, 3331, 3332.

Here are 3-collections.
1123, 1132, 1213, 1223, 1312, 1332,
2113, 2123, 2213, 2231, 2321, 2331,
3112, 3132, 3221, 3231, 3312, 3321.  

There is a natural way for you to check whether your understanding is correct without any extra effort, assuming you are required or scheduled to read that section "coupon collector problem" in the book. What you could have done is to try to understand that section as much as possible, assuming whatever interpretation your could have. If you find some inconsistency, then your interpretation is probably wrong. Otherwise, your interpretation is probably correct.

For example, I also doubted my understanding of that definition of $k$-collection. 

However, when I have read "if each box of a product contains one of a set of $M$ coupons, how many boxes must one buy, on the average, before getting all the coupons? This value is equivalent to the expected number of balls thrown until all urns have at least one ball or the expected number of keys added until all the chains in a hash table built by Program 9.1 have at least one key", I am confident that I got it correctly. I can imagine each letter in an $M$-collection is a box containing a coupon, where different letters mean different coupons. A ordered collection of letters is an ordered buying sequence of boxes containing coupons. So an $M$-collection means a buying sequence that gets all $M$ coupons right at its last buy. Ditto for chains in a hash table. The more I read, the more confident I become.