Commissions are commonly accepted as the term for "requests", when asking an artist (or other content creator) to create a piece of art specifically for you, usually based on your specifications, ideas or designs.
Since being an artist or content creator is commonly regarded as a profession, rather than a hobby, there is an expectation of commercial cost to a commission.
If the artist "does commissions", they are saying that they will accept requests for art, and will create that art in exchange for money. If the artist is "available for commissions", they are saying that they currently have the time (or, more likely, are actively looking) to take on these requests for art and expect to be paid at an agreed rate.
A patron who requests a piece of art or content, to a given specification, can be said to have "commissioned" it, so "I want to commission a few illustrations" is effectively, "I want to ask an artist to make special images for my needs and will pay them to do so."
Note that this is different from someone who purchases a piece of art that already existed, because they like the particular piece (or see potential future value in it), which is why the artist's statement also states that their "other work is for sale". The pieces for sale are likely ones that the artist has chosen to design and create themselves, or previous attempts at commissions that a patron did not choose to buy; while a commissioned piece is one that the patron has designed or described for the artist to create.