Blinking is a neat natural process whereby the eyelids wipe the eyes clean, much as a windscreen wiper on a car.
Blink rate tends to increase when people are thinking more or are feeling stressed. This can be an indication of lying as the liar has to keep thinking about what they are saying. Realizing this, they may also force their eyes open and appear to stare.
Blinking can also indicate rapport, and people who are connected may blink at the same rate. Someone who is listening carefully to you is more likely to blink when you pause (keeping eyes open to watch everything you say).
Beyond natural random blinking, a single blink can signal surprise that the person does not quite believe what they see ('I'll wipe my eyes clean to better see').
Rapid blinking blocks vision and can be an arrogant signal, saying 'I am so important, I do not need to see you'.
Rapid blinking also flutters the eyelashes and can be a coy romantic invitation.
Reduced blinking increases the power of a stare, whether it is romantic or dominant in purpose.