What's the purpose of the "outlines" around prints?
I am curious, what is the purpose of printing a single-height outline around the objects to be printed?


The (equidistant) lines at distance from the print object is called the "skirt", the skirt is an option found under the "Build Plate Adhesion" options in your slicer. The primary function of the skirt is to get the flow going, but there are more benefits you can get from the skirt:


You can find out whether the bed is correctly levelled, or if the bed has concave or convex areas (the skirt should be a line, I prefer at least 2 lines, of consistent thickness, if not, this may hint to incorrect levelling;
You can find out if there is enough or a sufficient amount of adhesive (e.g. glue stick, hair spray, specific print adhesion sprays like 3DLAC or DimaFix, etc), if not the bed might be greasy or lacking the adhesion product;
You can configure the skirt height to use the skirt as a shield for draft or ooze and distance to product);



  Also, how would it affect the outline if the object to be printed extends to (very near) the very edge of the print area?


Do note that a skirt limits the useable build area by the distance and width of the skirt.



Basically this has been answered (see this answer and this answer) in a different question ("Random lines are being printed?"), but it might be beneficial to answer this question rather than closing this for a dupe.  This question is focussed on the skirt, the equidistant lines around the print object, while the other question focuses on the priming line.