How to understand "to be better than a poke in the eye with a burnt stick"
how to understand it? dictionary tell me the meaning is "to be particularly welcome"

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It is a comical idiom that means something is not wonderful, but still acceptable.  Example:

"Do you want to go to a lecture on semiotics?"
"Well, I guess it's better than being poked in the eye with a burnt stick" (we also sometimes say "sharp stick" or "pencil," etc.).

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Thanks for Brad and Dorothy's answer. So it's terrible situation, so something I accept maybe better than it. so low standard.

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I've always heard it as sharp stick.