Something apposite is fitting or relevant. It is apposite that radio stations play Christmas carols on Christmas Eve, and that your tax accountant takes vacation after April 15th. It all makes sense.
The adjective apposite is derived from the Latin terms appositus and apponere. Ponere means to place, and thus apponere is "well-placed or well-put." Don't confuse apposite with opposite; they have almost opposite meanings!