Softness vs. sharpening: basically, it means that when magnified at over 100% some details in an image look slightly blurry, especially in the corners on full-frame cameras and particularly in the centre (all cameras). It begins with the lens' resolving power (not resolution), i.e., its ability to transmit details to the sensor. Anyone with a telescope will know what resolving power is. For example, if Barry Manilow lived opposite me and I trained a telescope on his bedroom at night, I would see that he wears a corset when he undresses. With a telescope with higher resolving power, I could read the washing instructions label on the corset. That's also the difference between a soft image and a sharp one. A soft image isn't blurry really. It just looks "flat". A really sharp image "pops".
Centre and corner sharpness is impossible at the lens' maximum aperture ("wide open"). Diffraction also affects sharpness at the other end (e.g. f/22). When photographers talk about a lens' "sweet spot", they refer to an aperture (and focal range) where the lens produces its best - and sharpest - results, usually somewhere between f/5.6 and f/11, although there are exceptions. The Canon 100 mm f/2.8 L macro mk II L IS comes to mind.
People forget that digital cameras are non-digital - the lens and the sensor are analog mechanisms that record light imperfectly. Firstly, light is bent, diffracted, distorted and generally messed about with in the set of glass components comprising the lens. Secondly, the sensor records photons, but the Analogue to Digital (A/D) converter is required to produce electronic (digital) files. In any conversion there is loss - for example, in the signal to noise ratio above, some of the details are lost as noise, but also in the analogue to digital conversion too as sharpness.
Next comes the issue of lenses. Generally speaking, expensive lenses are sharper than cheap ones. Prime lenses are sharper than zooms. A macro lens is necessarily sharp. No one expects compact cameras to have sharp lenses, although there are some exceptions.
Images can (in fact, must) be sharpened in post-processing. There is the counter-intuitively named "unsharp mask" filter in Photoshop and other image editors (it's a historic throwback to a technique used in film processing). There are other filters and gizmos that selectively sharpen your image. Perhaps the best known now is the "clarity" slider in Lightroom that sharpens your midtones.
All digital images must be sharpened, but not to the same degree. Portraits have to be selectively sharpened (eyes, teeth, glossy lips), with the skin softened. The best way to age someone is to push the clarity slider to the right in LR.
The following image demonstrates the difference between soft and sharp. It comes from my revenant account. If you look at the blow-ups, you'll see how terrible a Sigma 50 mm f/1.4 lens is for softness at max aperture on a full-frame DSLR.
Hope this helps.