The contents within the aside can be slightly or indirectly related to the content that it is adjacent to but be separate from it. You should be able to remove it and still have the other content make sense.
ARIA role attribute
There are a number of roles that can be applied to the aside element it would depend upon the content .
The aside element represents a section of a page that consists of content that is tangentially related to the content around the aside element, and which could be considered separate from that content. Such sections are often represented as sidebars in printed typography.HTML 5.1 Nightly
The element can be used for typographical effects like pull quotes or sidebars, for advertising, for groups of nav elements, and for other content that is considered separate from the main content of the page.
It's not appropriate to use the aside element just for parentheticals, since those are part of the main flow of the document.
Jeremy Keith says
..the aside element matches the concept of a sidebar HTLM5 for Web Designers and shows the example of a quote within an aside on page 66.
Bruce Lawson and Remy Sharpe in their book Introducting HTML5 gives an example of a <nav> and a <section> within the <aside>.