One easy way to do this is with puzzles. Sudoku, crosswords, word-finds, jig-saws. Also, games like Scrabble or Boggle that get you creating words out of random letters; and computer games that follow this same general idea. These kinds of games and puzzles get us focusing and really thinking, as well as sometimes using our memory, which is a fabulous work-out for our brain.
Something else that we've been finding extremely helpful for our brain, however, is a skill called mindfulness. Mindfulness is about living our lives in the present moment, focusing on one thing at a time in the present, and bringing acceptance to our experience. There are different types of mindfulness exercises and many different ways in which to practice; but over the past few decades we've been figuring out that mindfulness is incredibly helpful in many different ways. Just to name a few, mindfulness helps to reduce stress and can help with certain health conditions, as well as strengthen our immune system; it can help improve sleep; reduce symptoms of depression and anxiety; and helps provide that exercise that our brain needs in order to improve our concentration and memory.
Whole books have been written on mindfulness, so google it and you'll have no trouble finding more information on this tremendously helpful skill.