Don't want to have to cancel the cheque...

[Malapropist]

DH and I are going to a wedding in a few weeks and the invitation says, "No boxed gifts please, your presence is the only present we need!"

What does this mean? Should we give them some cash? Or do they really not want a gift? Wouldn't that be rude? It would feel weird to go to a wedding and bring nothing (except a card, obvs). What would you give? And if cash, how much!?

A bit of both.
I've put 'no presents please' on (birthday) invitations I've sent and genuinely meant it, but when I receive an invitation that says it, I tend to enclose some cash for them to treat themselves to something, as I don't feel it's right to go to a party of any kind empty handed.

So I'm no help

I suppose it would depend a bit on their circumstances, but I suspect the above applies - they are quite happy for you to come empty handed, it's up to you if you can bring yourself to do it.

No 'boxed' gifts is shorthand for 'but we'll accept a wedge of cash in an envelope'.

Slightly more tasteful than a poem, though.