'Search query' is relatively clever. Enter the words you want to match and stories with any of those words in them will be found. Prefix the term with a + to make it mandatory (+flower means the story must have the word flower in it) and a - to force it to not be there (-flower means no stories with the word flower in them will be returned).
Author is an author substring search and any author whose name has that text in it will be found. For example, just entering 'z' means any author with a 'z' anywhere in their name will be found. The same is true for title (story titles) and issue (story issue names)
The 'any of these tags' list will include any story that has at least one chosen tag. If you choose the "Aliens" and "Demons" options under creature then any story tagged with aliens or demons will be included.
If you choose a parent category then any story tagged with that parent or any of its children will be chosen. For example, if you choose "Creatures" then any story tagged with Creatures will be chosen, as will any story with "Aliens", "Demons", "Ghosts", and so on.
The "All of these tags" list marks the tags which are mandatory. A story must have all of the selected tags to appear in the story list. Unlike the "any of these tags" tag list, these tags are not expanded, and choosing a tag does not automatically choose all its child tags.
The exclude tag list will exclude any story that has one or more of the chosen tags. This does not include child tags, so choosing "Creatures" won't exclude "Aliens" or "Demons", just stories tagged explicitly with "Creatures".
Note that include and exclude selections apply even if the include and exclude forms aren't showing.
For example, if you wanted to choose all the MM stories that had either vampires or werewolves (or both), you would select MM in the "all of these tags" list, and "vampires" and "werewolves" in the "any of these tags" list. If you wanted to choose MM vampire stories that did not have demons you'd choose "MM" and "vampire" in the "all of these tags" list, and "demons" in the exclude tag list.