I've heard about that sometimes, Can anyone please give an example about robust and non-robust equity in terms of poker?

I think people use the term differently. I'm not sure there is a consensus honestly. I have heard people use the term robust to refer to hands that will maybe over realize equity because of suited connectedness; KQs has more robust equity than A3o even though A3o may be a favorite against KQs in hot and cold equity.

The other way I have heard it used is in situations where you have a hand with showdown value like QJ on AJ3 where your show down value is more robust then say A7s on 753 because, even though you have TP in the one hand, your show down value is not robust because its gonna lose a lot of its value by the river.

Hote that helps

Robust equity (which Matt Janda in particular talks about in his videos and books) basically just means the ability of a hand to maintain its equity (or "outs" if you want to look at it that way) even when betting makes villain fold some of his range and continue with his stronger combos.

For example, if you have 87ss on AT6 with one spade, you have a gutshot and BDFD. Even if villain has top two pairs or middle set, you'll still have at least a gutshot draw on the turn (and sometimes pick up the flush draw to go with it), and hitting the straight (or flush) will mean you always beat villain's sets/two pairs. Your equity with the gutshot is therefore robust, as you're drawing to a hand that is almost certain to win if you bink it. It has a realistic chance of beating the nutted parts of villain's range. That equity is only going to disappear if the board pairs on the turn, in which case you can re-evaluate.

Compare with a hand like 88 on AT6. If you bet with 88 (which isn't necessarily a mistake), and villain folds his low equity hands, you're not drawing to the nuts, and most turn and river cards will actually make your hand strength much worse, since they are more likely to help villain improve to a pair, two pairs or a straight, on the rare occasions where you were ahead on the flop. It's even possible that villain already has a set of aces or tens, and your only hope is to make runner-runner quads. 88 therefore does not have robust equity on AT6.

EDIT: I guess the cliffs would be: Robust equity means you have a hand that retains its equity well, and is likely to win at showdown even against ever-narrowing continuance ranges in big pot situations. Non-robust hands (mostly one-pair type hands) are likely to go down in relative hand strength as the pot gets bigger.

Thank you for your feedback guys