You are right, there has been a recent up tick in the number of work environments converting, at least partially, to standing desks. Although there are no rigorous studies of the health benefits of standing desks as compared to traditional desks, there is some anecdotal evidence that they may be helpful.
For example, people are likely to use bad posture when they are sitting at a traditional desk all day (slumping back in the chair, for example). This can contribute to neck and back strain and the development of chronic back pain. When you are standing, it is essentially impossible to have bad posture like this! Indeed, many supports of standing desks state that their back problems
have improved since converting over.
Another potential benefit of standing desks is that they break up the monotony of sitting at a desk all day. Many workers state that they feel more productive while standing, at least for part of the day; this no doubt has to do mostly with changing the routine and the effects that that has on the brain's level of alertness.
Finally, one theoretical benefit might be that you could burn a few more calories standing versus sitting, which could contribute to a healthier lifestyle overall.
Talk to your primary care doctor
for more information about how standing desks apply to your particular case!