갖다 is the spoken short form of 가지다, 'have or hold', and it rarely stands alone. Here it comes with a helper: 갖고 있다 (have it, own it), 갖고 다니다 (carry it about with you), 갖고 오다 (bring it), 갖다 주다 (fetch it and hand it over), 갖고 놀다 (play with it, or toy with someone). The -고 in front simply chains on the preceding action.