揽 has two distinct uses: physically pulling someone close (揽住) and figuratively taking on tasks or responsibility (揽活). 大包大揽 means to take everything upon oneself - often with the implication of biting off more than you can chew.
Left raise-hand radical (side form of 手) puts 揽 firmly in the manual-action family - pulling, grabbing, embracing - alongside 抱 hug, 抓 grab, 拉 pull, 握 grip. The hand drives the meaning here.
Right 览 supplies the sound - lǎn carried over unchanged. 览 itself means "to look at, survey," but in 揽 it works as a phonetic. Same sound: 缆 cable, 榄 olive. Combined with the hand: "gather into one's arms" - 揽客 attract customers, 总揽 take charge.
