It's an agreed period during which you stop paying the part of the mortgage instalment that corresponds to the principal and only pay the interest. Although it's less common, there's another type of grace period in which the entire instalment is deferred.
You can apply for a grace period when you take out your mortgage or at a later time, although the reason in each case will usually differ.
If you apply for a grace period when you take out the mortgage, it will probably be because of a shortage of liquidity as result of the initial outlay involved in buying a property.
If you apply for a grace period during the life of the mortgage, the reason will usually be related to temporary financial difficulties, for example if you have been made redundant.