Before you start theme development, I suggest you familiarize yourself with general WordPress Usage & Terminologies.
Taxonomy:
In general taxonomy means classification.
In WordPress, posts, pages, custom post types etc. can be further classified by using different taxonomies. For example, you may have hundreds of blog posts. Now how do you classify them for better arrangement? You use category, tags to do that. So tags, categories etc. are WordPress defined taxonomies.
It’s also possible to define custom taxonomy using CODE or existing plugins. What you do with it depends on your needs.
For example, you write about movies in your website (among other things). Now, instead of classifying movies based on WordPress defined categories and tags, you may create a your own taxonomy called genre. Since one movie may fall under multiple genre, you can create it so that it behaves like tags.
Now if a visitor to your site wants to see all posts from say action genre, she’ll be able to do so simply by selecting that genre. As a theme developer, you may provide custom templates for genre taxonomy so that users may get appropriate look and feel that goes well with a movie genre.
Query:
Every dynamic website needs database & as a developer, sometimes you’ll have to get information from the database to show to the users. In WordPress Query simply means asking specific information from the database.
For the most basic information gathering from theme templates, WordPress has a default way of getting data as needed, this is called the loop. In the loop, WordPress does the database query internally so that you may present related data in templates using simple functions, called template tags.
However, if you need more information from the database than WordPress provides by default, then you’ll have to use custom query to get that.
Further Reading:
Once you’ve familiarized yourself with WordPress terminologies and features (as provided in the beginning), I suggest you study The Official WordPress Theme Development Guide.