What is the meaning of 싶다?

to be desirous of, to want

Used after a clause with a sentence ending that expresses a sentiment or subjective speculation, commonly ㄴ가 (-n'ga), (-na), ㄹ까 (-lkka), 으면 (-eumyeon), and (-da), to state that the subject feels that certain way.

Source: wiktionary.org