欢 (traditional 歡) has 欠 on the right — a person with an open mouth, exhaling or singing. The whole character is about open-mouthed delight: joy, merriment. The simplified form swaps in 又 (a hand) on the left for an easy shape.
欢 means joyful, and joins 喜 to make 喜欢 (to like) — one of the first verbs every learner needs: 我喜欢… (I like…). It also gives 欢迎 (huānyíng, 'welcome' — 'joy-meet', the sign on every shop door), 欢乐 (joyous), 欢笑 (laugh merrily). Where 喜 is the joy felt, 欢 is joy expressed out loud and shared. Together, they're 'to like' — the warmth you feel toward what delights you.
An open mouth (欠) in delight — JOY, merriment.
欢迎 ('joy-meet') is 'welcome' — the two characters on the door of every shop and home in China. 喜 + 欢 = 喜欢, 'to like'.