The narrator of the story, the young tearaway Smith, is reminiscing about the time when he and some cousins of his got into trouble when they were younger. One hot summer's day, Smith and the other boys were romping through the countryside, wandering through the fields and scrumping apples. They then came across a middle-class family enjoying a picnic. Suddenly, Smith and his cousins dashed out from behind a bush and grabbed as much of the family's picnic food as they could lay their thieving hands on before running off.
Looking back on this episode, Smith feels that the well-to-do-kids whose picnic he ruined should've felt the same way as he's felt throughout his whole life: like some big boot is about to smash any nice little picnic he might make for himself. What he means by this is that anything good in his life is always likely to be ruined at any moment. For him, the big boot symbolizes the nasty habit life always seems to have of destroying anything good, any "picnic" that Smith might be enjoying. For Smith, life has been one long succession of "big boots," and in ruining the posh family's picnic he was making them feel exactly how he's felt at every moment of his life.