Minimum volatility indices are not widely used, with only the MSCI ones widely used. However, they are likely to become more widely used given the general trend towards using style indices whenever appropriate, and increased interest in minimum variance portfolios.
A minimum volatility index will give higher weightings to lower volatility securities (usually these equity indices). The MSCI indices use the covariance of each share against all others in the index.
Proponents of minimum variance strategies claim that the good performance of minimum volatility indices, especially when measured using risk adjusted measures such as the Sharpe ratio. The problem with most such claims is that they are based on periods of weak market performance. However, there are much longer periods when low variance strategies performed well, which is perhaps unsurprising given that there is also strong evidence for the value effect.