Zero dividend preference shares, often called zeros, are simply preference shares that do not pay an annual dividend. They instead simply redeemed for a lump sum at a fixed date.
Zeros are similar to zero coupon bonds. They are more risky because they are shares and therefore rank lower than bonds for repayment if the issuer is wound up.
To look at this another way, consider how the present value of a zero will change if the risk changes. With a single payment a long way off in the future, even a small change in the discount rate will have a large impact on the value. Therefore a small change in the risk premium will mean a large change in the value.
Zeros gained something of a bad reputation due to problems at a number of British split capital investment trusts that come to light in 2002. This was due to the way in which those particular trusts were managed, and does not say much about the intrinsic qualities of zeros - except perhaps highlighting a need for transparency to allow proper valuation of different classes of share.