What P0101 means
Your car has a mass air flow (MAF) sensor sitting in the intake tract, right after the air filter. Its job is to measure how much air is coming into the engine so the computer can mix in the right amount of fuel. P0101 means the signal from that sensor is not behaving the way the computer expects. It is not necessarily saying the sensor itself is bad. It is saying the reading is out of range, or does not track properly as the engine changes speed and load. That could be the sensor, or it could be something upstream or downstream of it fooling the sensor into giving a bad reading.
Is it safe to drive
Usually yes, at least for a while. Common symptoms are rough idle, hesitation on acceleration, poor fuel mileage, or the engine feeling like it's running rich or lean. Some cars go into a limp mode with reduced power. Watch for stalling, especially at idle or low speed, and for the check engine light turning solid or starting to flash. A flashing light means misfire and you should stop driving and get it looked at sooner rather than later. Otherwise, get it diagnosed soon, but it is not an emergency today.
Common causes, most likely first
A dirty or contaminated MAF sensor is the most common cause. This happens a lot on cars that have had an aftermarket oiled air filter, or where the filter has been left dirty too long. Cleaning it sometimes fixes the problem outright.
After that, look at the intake tract itself: a cracked air intake hose, a loose clamp, or a poorly seated air filter housing can let unmetered air into the engine and throw off the reading even with a perfectly good sensor. Vacuum leaks downstream of the sensor do the same thing.
Wiring and connector problems are also common: a corroded MAF connector, a rubbed-through wire, or a bad ground can produce a range/performance code without the sensor being faulty.
Less commonly, the sensor itself has failed electrically, or on some engines a dirty throttle body or a failing fuel system component confuses things enough to trigger this code. Which of these is likely depends some on the specific engine and how it routes its intake air, so it is worth having someone look at the actual car rather than guessing from the code alone.
Diagnosis and rough cost
Diagnosis starts with pulling live MAF data on a scan tool while checking intake hoses, clamps, and the sensor connector for damage or corrosion, before assuming the sensor is bad. That inspection and test drive is usually a shorter diagnostic job. If it turns out to be a vacuum leak or hose, repair cost is generally on the lower end. A new MAF sensor costs more, and cost varies a fair amount by make and model. We would not recommend replacing the sensor until the wiring and intake tract have been checked, since a lot of these codes turn out to be a leak or a dirty sensor rather than a failed part.