Angels and demons have a very different idea of intimacy than humans do— they think the rituals created by humanity are rather shallow, seeking skin-on-skin contact as opposed to anything celestials consider to be genuine affection. Instead, most of their displays of love are based around their wings. Take, for example, preening: wings are very delicate, sensitive things, and thus preening them is a very delicate and sensitive process. Letting someone else in on such a personal affair is incredibly intimate, indulged only in private. (I’m trying to keep this headcanon general but I very much feel the need to point out that such is the case especially for Crowley, who is so protective of his wings that it takes him ages just to warm up to the idea of even showing them to Aziraphale. To say Hell hadn’t treated them kindly is so understated that to call it an understatement is almost offensive, and unfurling the things terrifies him. Eventually, though, he relaxes enough to allow the angel to return the favor he’s been giving for so many years.) Touching wings together is also a display of affection and can best be likened to holding hands, but it carries more weight to it than holding hands does— it’s never just a casual thing between friends, though it can be platonic. More definitively romantic is the tradition that partners will often keep a small feather from their significant other’s wing somewhere on their presentable form, often times in some sort of tasteful earring or necklace (Aziraphale keeps Crowley’s on the chain for his pocket watch and Crowley keeps Aziraphale’s around his neck, neither of which are ever separated from their persons).
Additional to all of that is a small patch of skin between where their wings are when unfurled that, when pressed or stroked, calls forth the wings of the celestial in question. The act of doing so also causes the celestial to still, if only just for a moment, meaning the weakness is very useful in battle. Consequently, traditional battle attire includes a hard plate over that area to prevent anyone from performing such a maneuver. Outside of war, it takes on more intimate implications: by allowing someone to touch it you are trusting them not to harm you or your wings in that brief moment of paralysis. (Aziraphale has done it multiple times to Crowley, often times to slow him down when he’s spiraling into a panic. He’s also done it on more petty occasions, when the demon refuses to let himself be preened when he knows he should be. Crowley has done it to Aziraphale a grand total of once, having found the angel a frantic mess in his bookshop a few days after their trials.)