STF stands for "Smooth Transition Focus", and is a Sony-specific* term indicating that the lens includes an apodization filter to create smooth bokeh (out-of-focus blur) — and smooth bokeh is generally considered to be the best bokeh. So, you'd generally use it for non-studio portraiture or in other cases where that blur is an important artistic element.

Other lensmakers use different terms; for example, Fujifilm designates their lens with this feature "APD".

Note the t-stop designation of T4.5. This indicates that the actual transmission of light at the widest aperture is that of a theoretical f/4.5 lens — even though the effective maximum aperture is f/2.8. That's because about a stop is lost to the filter. (Fujifilm's f/1.2 APD lens is similarly limited in this way, with a t-stop of 1.7, again about one stop lost.)

Read more about t-stops at What is T-number / T-stop?. This concept is used for any light loss (which all lenses invariably have, since they're made of real-world materials), but normally the difference is small enough that we just ignore it — see Why are DSLR lenses measured in F stops instead of T stops? for more on why. But with the apodization filter, there's enough of a difference that it can be important to be aware. Any through-the-lens autoexposure program mode will take this into account automatically; if you are doing manual metering and calculations, you should figure it in (although of course these digital days it's easier to guess and check than worry about the numbers).

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* Previously, a Minolta-specific term, and then Sony bought Minolta's camera business....