A risk measure comparing the change in the price of the underlying asset to the corresponding change in the price of a derivative. Regarding call options, a delta of 0.5 means that for every £1 the underlying stock increases, the option will increase by 50p.
Put option deltas will be negative, because as the underlying stock increases in value, the value of the option will decrease. So a put option delta of 0.5 means that for every £1 the underlying stock increases the value of the option will decrease by 50p.