When two RF signals are input to an RF component such as an LNA or a Mixer, it results in the creation of other mathematically-related, spurious signals. This is a result of non-linear behavior of the component. Spurs cause distortion and affect the quality of the output signal.
These spurs occur at different combinations of the input signal frequencies. In the picture below, you can see that spurs created at the output of the LNA fall at varying frequencies relative to the two main signals. Third-order spurs fall closest to the input signals. Spurs other than third-order can be eliminated with filters. Third-order spurs are most difficult to eliminate as they fall so close to the signals of interest.
IP3 stands for third-order intercept point. It is a mathematical figure of merit of the linearity of an RF component. The more linear a component, the higher the IP3. In general, you want your components to be as linear as possible. For instance, out in the real-world, you want your LNAs to be able to withstand strong signals without distortion.
The folks at Shure microphones have explained intermodulation within the context of their wireless microphone systems. As you will see, things get increasingly complicated with the number of input signals and how that in turn increases the challenge of frequency coordination.
IP3 is a specification that tells you how linear an RF component is. For instance with an LNA a higher IP3 implies greater linearity and in turn a better ability to withstand strong signals in the field without distortion of the desired signals.