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), 나 (-na), ㄹ까 (-lkka), 으면 (-eumyeon), and 다 (-da), to state that the subject feels that certain way.
Source: wiktionary.org