This pattern indicates a remarkable or uncommon condition in a positive or negative sense or expresses the severity or magnitude of the verb.

- used with descriptive verbs

Examples:
기삐기 짝이 없어요./I'm happy beyond measure.
미안하기 짝이 없습니다./I'm terribly sorry.
방은 더럽기 짝이 없더군요./Your room is dirty beyond belief.

Note: this aren't literally translations of this pattern. Rather this pattern expresses the severity of the situation and so you have to use some strong superlative when translating it into English.