The fact that an antenna is designed for a specific frequency, or resonance frequency, does not mean it is unable to transmit or receive signals from other frequencies.
Any antenna has a bandwidth, which is the range of frequencies where the antenna is able to operate with acceptable efficiency.
To determine the bandwidth of an antenna, or how well they behave for a given frequency, there are different parameters. The simplest to understand is the reflection parameter, which measures the amount of energy reflected by the antenna. If the antenna is perfectly matched to the transmitter, it will use 100% of the energy that the transmitter delivers. As this adaptation become worse (by the design of the antenna, or because we wish to transmit a frequency that is not the resonant one), the antenna will reflect a higher percentage of the energy delivered by the transmitter.
The following graph shows the reflection parameter of an antenna designed to resonate at 2440MHz.
At 2440MHz we can see that the reflection parameter is -18.59dB, which means in linear units that it reflects 1.38% of the power, taking advantage of the 98.62% of the power.
The following table shows the equivalence between the reflection parameter and the percentages of reflected power and coupled power.
We define the bandwidth of the antenna as the frequency range for which the reflection parameter is lower than-10dB, or in other words, the reflected power is less than 10%, resulting in a frequency band where the efficiency is bigger than 90% (90% of the power delivered by the transmitter is used in the antenna).
As shown in the graph above, this antenna has a bandwidth from 2258 MHz to 2796 MHz.