What is an 'approach invitation'? Well, first of all, I don't really like the term 'approach invitation', as it has connotations of PUA style terminology, but for the purpose of this post it serves its use. An 'approach invitation' is any 'sign' or 'signal' a woman gives you (usually non-verbal) that she finds you attractive and wants you to approach her.
The most common of these is eye contact, often followed by a smile, or the 'double-take' eye contact, i.e. when you look a girl, she looks at you, you or her then look away and then you look back at her and she looks at you again (and possibly smiles at you again). Maybe you've had this happen to you when you're walking down the street or you've been sitting somewhere in public. This is universally understood as a woman saying 'I find you attractive and I want you to approach me'.
It's all good and well approaching a woman when you get a sign like this, however a lot of women when they're out and about and going about their business don't always give out these 'approach invitations' as they're just too busy doing other things. They could find you attractive, but they could be caught up in their own world, thinking about what errands they have to run etc, and so they probably won't be thinking about giving out signals to guys they think are attractive as they walk down the street.
And if you wait around for them to give you 'approach invitations', you're going to miss out on a lot of women who would probably be delighted if you'd approached them....but you didn't approach them because you were stupidly waiting around for 'approach invitations'.
Of course, if a woman DOES give you a sign she wants you to approach, get over there immediately and be direct.
A true Direct guy doesn't wait around for 'approach invitations'. He takes the bull by the horns and approaches whatever girls he wants, without waiting about for 'signs' and 'signals' from them.