In the world of finance, dilution means something is being watered down, typically earnings per share (see separate definition).
Warrants, share options and other convertible securities issued by a corporation have a potentially diluting effect on earnings per share because more shares are created without any boost to earnings.
Say, for example, a company has 100 shares in issue and earnings of £20. EPS is 20p. It then issues a further 100 shares to meet demand from options being exercised. Since there is no associated change in earnings, the revised EPS figure is now £20/200 or just 10p.