What are these attributes: `aria-labelledby` and `aria-hidden`

The primary consumers of these properties are user agents such as screen readers for blind people. So in the case with a Bootstrap modal, the modal's div has role="dialog". When the screen reader notices that a div becomes visible which has this role, it'll speak the label for that div.

There are lots of ways to label things (and a few new ones with ARIA), but in some cases it is appropriate to use an existing element as a label (semantic) without using the <label> HTML tag. With HTML modals the label is usually a <h> header. So in the Bootstrap modal case, you add aria-labelledby=[IDofModalHeader], and the screen reader will speak that header when the modal appears.

Generally speaking a screen reader is going to notice whenever DOM elements become visible or invisible, so the aria-hidden property is frequently redundant and can probably be skipped in most cases.

aria-hidden="true" will hide decorative items like glyphicon icons from screen readers, which doesn't have meaningful pronunciation so as not to cause confusions. It's a nice thing do as matter of good practice.

HTML5 ARIA attribute is what you're looking for. It can be used in your code even without bootstrap.

Accessible Rich Internet Applications (ARIA) defines ways to make Web content and Web applications (especially those developed with Ajax and JavaScript) more accessible to people with disabilities.

To be precise for your question, here is what your attributes are called as ARIA attribute states and model

aria-labelledby: Identifies the element (or elements) that labels the current element.

aria-hidden (state): Indicates that the element and all of its descendants are not visible or perceivable to any user as implemented by the author.