When you send some kind of radio signals at some frequency say 5 GHz to a repeater and it transmits it back at higher power, what change is made to the radio signal? For example: Will it be transmitted back at higher frequency or in what terms it is said to be amplified? How do you measure its strength?
All electromagnetic signals that leave an antenna have an amplitude, i.e. there is power propagating as they spread.
power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit time.
The signal which the waves are carrying is a pattern on this propagation of energy. As energy is transmitted from the original antenna, the power falls as 1/r^2, so, as the distance grows the signal also becomes weaker in strength/energy, smaller in amplitude.
A repeater boosts the power once more, keeping the signal shape on the electromagnetic carrier wave but restoring the amplitude to levels detectable by radio/tv/mobiles...
The frequency pattern is kept unchanged because it is the one carrying the message and the tunability.
This is basically the same as Anna's answer but worded differently;
A radio wave is characterised by two parameters, it's frequency and it's amplitude. The amplitude is the "strength" of the wave i.e. if you connect a multimeter to an aerial then the greater the wave amplitude is, the stronger will be the voltage you measure on your multimeter.
So a repeater just retransmits the signal at the same frequency but with the amplitude multiplied by some factor. The more powerful the repeater the more it multiplies the strength of the signal.