What does it mean?

In my case, it is a means of letting my wife know that I love her, that I just remembered another reason why I love her, that I am glad to be with her, not someone else and that I am thankful she is willing to let me be the one holding her hand, instead of someone else. I do try to make sure I don't squeeze hard enough to hurt her though.

It's a comforting gesture. It's to let you know that he's still got you and cares, and for him it also reassures him that you're still there. It chases away any minor loneliness and also just makes you feel good.

He just really wants to hold on to you. Glad your his.