As we age, our brains tend to slow down―a concept known as “neural slowing.” One side effect of neural slowing is that oftentimes our brains lack the ability to track the faster moving parts of speech, making it harder to hear. This degraded processing ability is especially heightened in environments with a lot of background noise. A study out of Northwestern University  has demonstrated that specialized, auditory-based training for older individuals can help counteract neural slowing and improve the ability to successfully hear, remember, and understand sentences in noisy environment.
Keeping your brain stimulated and active is increasingly important as you age. You should speak to your general practitioner about any sort of serious cognitive training you want to undertake, however there are some easy ways to get started in the meantime. Daily crossword and Sudoku puzzles in your newspaper or on online apps are a great way to get your brain thinking analytically. Really, any sort of logic puzzles you enjoy could be useful.
Similarly, there are some auditory-specific hearing exercises you can try. In order to help you focus on specific sounds above background noise, try creating an environment where you must practice just that. Set up noise making devices like a laptop or a tape player in different parts of the room and turn them on. Then have a friend read to you from a book or magazine article. Try to focus only on the words that they are saying. Another fun hearing exercise is trying to locate where sounds are coming from in space. You can do this anytime you hear a noise around you like a bird tweeting or a car horn. Just try to pinpoint where in your environment that distant sound originated from.