The image you sent is of a Solitaire board game set. Solitaire is a single-player puzzle game played on a board with holes and pegs or marbles. The goal of the game is to jump over other pegs and remove them from the board until only one peg remains. Here are the specifics of the game in the image:
The board is made of wood.
There are 33 holes on the board, arranged in a cross shape.
There are 32 glass marbles included in the set.
here are the general rules of how to play Solitaire:
Set up the board by placing a marble in each hole except for the center hole.
Select a marble to jump with.
Jump the selected marble over an adjacent marble to a vacant hole. The jumped marble is removed from the board.
Only jump marbles one space at a time, either horizontally or vertically.
The goal is to jump and remove all the marbles from the board except for one.
There are many different variations of Solitaire, so the specific rules might differ slightly depending on the version you have.