"I like going shopping."
It's a very particular grammatical construction.
Verb stem + に + directional verb such as come/go = To go to do something.
I.e. 映画を見に行きます would mean "(I'm) going to see a film" since 見（み） is the stem of 見る.
Suru nouns are even easier in that as in the above construction you can just say Noun + に + 行く/来る.