There is this weird thing in photography called "Bokeh" - often misunderstood as synonym for shallow depth of field. Yes, it is related to depth of field, but it is by far not the same. Bokeh is a Japanese word which means blur or haze, and is here in photography related to some artistic quality of the blur. The appearance of the bokeh effect mostly depends on the lens construction itself and the form of the lens aperture shapes. The more wide open the aperture, the better the bokeh normally - it is visible as circular patterns in the highlighted  blurred background of a photo. The Christmas Light photo below demonstrates this effect with the circular pattern in the background. The photo was taken wide open at f/2.0 with a 135/2.0 lens.

It is mostly a matter of taste to like this effect or not - I personally love a beautiful and especially colorful bokeh effect in photos taken with a wider open aperture. Bokehs can look fairly unattractive at smaller apertures due to less circular shaped patterns (which means there are more edges visible leading to polygonal shapes and hard-edged bokeh). The more aperture blends a lens contains - preferably even with rounded edges - the better looking is normally the bokeh effect. The photo on the right was taken purposely to create this out-of-focus effect (135/2.0 at f/2.0).

How can we explain this effect from a technical point of view? In out-of-focus areas each point of light displays an image of the aperture of the lens, normally a round disc. Depending on the lens construction and the aperture used for the photo, you might see big full circular shapes, oval ones, or donut-like discs. The brightness of this disc largely depends on the lens correction, too (it means how they are corrected for spherical aberration). Some modern lenses use so called apodization filters to even enhance a smoother looking bokeh effect. 

Often bokeh effects appear in the photo unexpectedly. When I took the shot shown below of a mockingbird (which was fairly aggressive against me when I disturbed it), I later found the nice looking bokeh discs on the left which fitted perfectly to the overall composition. This photo was taken at 400 mm focal length at a smaller aperture of f/7.1.

In my experience, the best bokeh effects can be often achieved by highlighted backgrounds, sun reflections from the side hitting foliage/leaves, light reflections on water or other shiny surfaces. You might see that some of your lenses are better than others in your collection to reveal a beautiful looking bokeh.