You have the regular expression $(((a^*b)b)\cup b)$. The subexpression $(a^*b)$ generates the words $b,ab,aab,aaab$, etc., because $a^*$ generates any string of $a$’s, including none at all. These words can be described in English as the words over the alphabet $\{a,b\}$ that contain exactly one $b$ and have that $b$ at the very end. Alternatively, they are the words that start with any number of $a$’s (including none) and then have a single $b$.
Let’s build up to the next larger subexpression: $((a^*b)b)$ takes any word generated by $(a^*b)$ and tacks a $b$ on the end, so we now get $bb,abb,aabb,aaabb$, etc.; these are the words that start with any number of $a$’s, possibly none, and then have $bb$. Alternatively, they could be described as the words that end in $bb$ and have nothing but $a$’s before that.
The subexpression $b$ on the right of the union of course generates only one word, $b$.
Finally, the union in $(((a^*b)b)\cup b)$ gives you everything generated by $((a^*b)b)$ or by $b$, so you get every word that ends in $bb$ and has nothing but $a$’s before that (if anything), and in addition you get the word $b$.