impedance matching
Impedance matching is choosing or building things so a source, a line, and a load all agree on the same impedance, so power flows across the joints cleanly instead of bouncing back. A homely picture: matching is like choosing a hose nozzle that neither chokes the flow nor lets it spray uselessly, it is sized to pass the water smoothly. In RF the goal is to make the load look like the line's characteristic impedance, usually 50 ohms, so the reflection coefficient goes to zero and no standing wave forms.
There are two related reasons to match, and they are worth separating honestly. The first is to kill reflections on a transmission line: if the load equals Z0, the wave is fully absorbed, VSWR is 1:1, and all the delivered power is used. The second is maximum power transfer: a source delivers the most power to a load when the load impedance is the complex conjugate of the source impedance. For a purely resistive 50 ohm source feeding a 50 ohm load these two ideas coincide. But remember the honest catch from low-frequency theory, matching for maximum power transfer delivers only 50 percent efficiency, so RF matching is about getting weak signals across cleanly, not about efficient bulk power delivery.
Matching is done with networks of inductors and capacitors (an LC matching network), with quarter-wavelength line sections, or with transformers, each transforming one impedance to another at a chosen frequency. It is essential at every RF interface: between an antenna and a feedline, between a transistor's awkward input impedance and 50 ohms, between stages of a receiver. Honest caveat: a match is built at a particular frequency and degrades as you move away from it, so wideband matching is harder and always a compromise. And matching transforms impedance, it does not create power, you are routing the available signal efficiently, not amplifying it.
A transistor's input might look like 10 ohms in series with some capacitance, which a 50 ohm source cannot drive efficiently. A small LC network is inserted to transform that 10 ohms up to 50 ohms at the working frequency, so the source sees a clean 50 ohm load and maximum signal reaches the transistor.
A matching network transforms an awkward impedance to the system value, here 50 ohms.
Matching transforms impedance at one frequency; it does not add power and does not hold across a wide band. Maximum-power-transfer matching is only 50 percent efficient, so it is for signal integrity, not bulk power delivery.