inertial frame
An inertial frame is a frame that is not accelerating — it neither speeds up, slows down, nor turns. Its defining test is Newton's first law: in such a frame an object with no force acting on it either stays still or coasts along a straight line at steady speed. If left-alone things drift sideways or curve for no apparent reason, your frame is not inertial.
You can feel the difference in everyday life. Standing in a smoothly cruising train, a coin balanced on your hand stays put, just as it would on solid ground; the train's frame is (very nearly) inertial. But the instant the train brakes, the coin lurches forward with no hand touching it — that sudden pull reveals an accelerating, non-inertial frame.
Special relativity is built entirely on inertial frames, because they form a privileged family in which the laws of physics take their simplest, identical form. Strictly, no real frame is perfectly inertial — Earth spins and orbits the Sun — but a freely floating laboratory far from gravity comes very close, and on short timescales a lab bench is good enough.
A frame is inertial exactly when free bodies coast in straight lines at steady speed.
Einstein's equivalence principle later shows that a frame in free fall under gravity also behaves like an inertial frame locally, while a frame standing still on the ground does not — a clue that gravity is special.