You've probably heard that the brain uses a disproportionate amount of the body's power budget -- the average for an adult is about twenty watts. Unless you're a serious athlete this is about a fifth of your power consumption (for children the figure is about half!). I used to wonder if this increases when you're doing a lot of mental work, but it turns out the impact is very small - Einstein was about the same sleeping as he was during his most productive moments. It turns out there's a neat reason for this
Your brain has about 86 billion neurons. They're all firing regularly at a low level to stay alive, but when they're engaged there's a spike of activity and power consumption. In fact only about one percent of your neurons are spiking at any given moment. You have a mechanism that regulates how many neurons can fire .. it's complex, but basically attention is used to direct what's spiking and what's just idling along.
Even though our senses only sample a small amount of the natural world around us, the amount of information is still far too much for our brain to handle. Picking out one voice at a party, being interrupted by a fire alarm, following the ball in a sporting event amidst many players and a huge crowd. We're good at identifying what might be important and ignoring the rest. By focusing our attention on something we process that information and ignore the vast majority of what's coming in.
There are two basic attention mechanisms. Voluntary and involuntary. Focusing on the car in front of you can be voluntary. Looking at the dashboard and suddenly catching a brake light out of the corner of your eye lights up your involuntary attention. Voluntary attention requires about a third of a second to process signals. Involuntary is much faster - about a tenth of a second. One can imagine good evolutionary reasons for the bias.
Without attention our brain's power consumption would be something like two thousand watts with over one hundred times as many neural spikes. The energy that runs the neurons is turned into heat which has to go somewhere. At twenty watts our brains require an elaborate water (well, blood) cooling system. A medium sized heating element on an electric stove is about fifteen hundred watts, so your full throttle brain would cook and then burn. Approximately unhealthy.
You can make your brain more efficient at certain tasks through mental and physical exercise. Play an instrument, learn another language, become proficient at a sport, learn how to do math .. all of these will create more efficient neural pathways to improve your ability. It's a separate subject, but creativity in an area may be linked to having well developed very different regions and waiting for cross talk. (one of the big reasons I'm not comfortable with an extreme focus on STEM education).
Sudden involuntary attention fires enough neurons to force those you've been using for something else to shut down. If the task involved a chain of thinking it's very difficult to spool up and recreate your original path. Multitasking is less efficient that working on one thing at a time. It's worse when an involuntary interrupt arrives. When you have to concentrate or even engage in productive daydreaming, you should reduce the likelihood of involuntary interruptions. Like concentrating on a single voice at a party, you can get good at ignoring background "white noise" below a certain threshold.
So keep your brain at twenty watts, create powerful new wirings and know when to isolate yourself from all of those interruptions. And stay away from attention rewiring/brain chilling:-)