selectivity is the ability of a sensor to measure a concentration of a substance in presence of other interfering substances.
sensitivity is the slope of the calibration curve i.e. how much does a change of concentration affect the change of receiving signal (e.g. electric current)
I didn't really come across the term cross-sensitivity so I can't help with this one.
If a sensor can detect the concentration of two or more substances, or other parameter, for example, temperature, it said the sensor with a cross sensitivity.
Let's start with sensitivity first then selectivity and cross-selectivity.
Sensitivity - It is the ability of the sensor to respond to input changes. In other words, how fast or high the output (say for example, electrical quantity such as volts or resistance) changes in response to the change in the concentration or level of the input quantity or parameter. Take for example, you have a resistive gas sensor then sensitivity can be defined as what is the % change in resistance with reference to the change in input gas concentration.
Selectivity - It is the ability of the sensor as how well it discriminates the response from the adjacent inputs. So in our example gas sensor if it is designed for methane then HOW WELL will it respond to methane in presence of other gases. The response is usually like a Gaussian curve or ideally it is expected so.
Cross-Sensitivty - It is the sensitivity of the sensor to other gases (alone) not a mixture of gases or input parameters.
Hope you will find this helpful. Will be happy to answer any clarification.