What does it mean when a woman tells a man she is dating she needs him?

Just that,she needs him in some way.

It could be many things.

She may need his affection which means she may want him in her life. OR she may just want his presence as a friend and not be lonely.

It means he should take his Amex card with him.

Depends on context and on people involved.

she likes his company

More intimate maybe?

Emotional blackmail?