What people mean by brain training
Brain training usually means short games or exercises built around a mental skill: remembering a sequence, doing sums quickly, spotting a pattern, or ignoring a distraction. Most apps mix several skills and track your scores as you improve.
What the research says
The clearest finding is that practice makes you better at what you practice. If you play a memory game every day, you get better at that memory game.
The harder question is transfer: whether getting better at a game makes everyday thinking easier. A large 2016 review in Psychological Science in the Public Interest, led by Daniel Simons, found extensive evidence that training improves performance on the trained tasks, less evidence for closely related tasks, and little evidence that it improves everyday cognitive performance.
Some long studies have found lasting effects on the trained skills themselves. In the ACTIVE trial, a randomised study of 2,832 older adults in the United States, people who had ten sessions of reasoning or speed training still scored better on those skills ten years later, and somewhat more of them reported that everyday tasks were as easy as at the start. Memory training didnât keep its effect on memory in the same way. That was a specific program for older adults, not an app.

Knowledge
Language
Reasoning
Numbers
Memory
Focus