In Macbeth, what do the witches equate fair with? What does paradox mean?

The witches use this expression at the beginning of the play when they have come together to plan their mischief:

Fair is foul, and foul is fair:
Hover through the fog and filthy air.

They compare fair to foul, equating the two. Foul means filthy, dirty, bad or any number of synonyms which refer to something disgusting or evil, whilst fair is a reference to something good or beautiful. In essence, what the witches are saying is that what is bad is good and what is good is bad. This is a paradox.

A paradox may be defined as a statement or expression, or even an event or situation, which may seem to be absurd or a contradiction in itself but proves, on closer investigation, to actually contain a profound truth. An example would be 'Ignorance is bliss' which implies that not knowing something, ensures happiness. As, for example, in a situation where a person who is happy in a relationship is unaware that his or her partner is involved in an illicit affair. Since he or she is ignorant of this fact, he or she remains happy. 

In Macbeth, this paradox is a recurring motif throughout the play. He himself also comments later:

'So fair and foul a day I have not seen'

He means that the day is good because they were victorious and foul since so many were killed and the weather is bad. This ties in with what the witches said at the beginning.

Macbeth, himself, is caught in a paradox. At the beginning of the play he is praised for his noble qualities: courage, loyalty and determination. He is a man of integrity and is seen as good, yet he is the person who, with his wife, commits the most horrendous of crimes, the assassination of his king. So the one who is deemed fair (good) turns out to be foul (malicious). Once he commences on this path, he becomes virtually unstoppable and his tyranny spreads like a disease throughout Scotland.

The witches, as servants of evil, use paradoxical statements throughout the play to deceive and manipulate Macbeth and lead him deeper into evil and towards his own doom. They, for example, tell him through an apparition:

Be bloody, bold, and resolute; laugh to scorn
The power of man, for none of woman born
Shall harm Macbeth.

Macbeth understands this as meaning that he is invincible, for all men and women are of women born. He therefore does not have to fear anyone.

The equivocal nature of this statement becomes horribly clear when he faces Macduff on the battlefield and declares:

Let fall thy blade on vulnerable crests;
I bear a charmed life, which must not yield,
To one of woman born.

Macduff, however, replies:

Despair thy charm;
And let the angel whom thou still hast served
Tell thee, Macduff was from his mother's womb
Untimely ripp'd.

It is only then that Macbeth realizes the true meaning of the witches' deception. Macduff was not born by natural means (he did not pass through the birth canal) but was cut out of his mother's womb.

In the end, it is Macbeth's own foolish lack of insight which leads him towards tragedy. He becomes a bloodthirsty dictator and it is this evil that finally destroys him.