Gummed brown tape is a type of tape made from brown paper that has dried glue on one side which you wet with water to activate (like you moisten the glue on an envelope to seal it).
Gummed brown tape is commonly used to stick down the edges of watercolor paper when you stretch a sheet of paper to prevent it warping when you paint.
The shiny side is the one with the glue on. Use a piece of sponge or wet cloth to 'activate' the glue rather than licking it. Keep a separate sponge/cloth for doing this to getting glue on your sheet of paper.
Gummed brown tape sold in rolls in various widths. If you're a beginner in terms of using it to stretch watercolor paper, start with a wider tape, it's easier.