Falsifiability is the ability for something to be proven wrong or be proven false. This concept was first introduced by scientist Karl Popper (1902-1994) whose interest focused on how to properly separate real, legitimate science from pseudo-science. Now falsifiability is typically used in regards to the scientific method and empirical testing. If something exhibits falsifiability and is falsifiable then it can be proven wrong.
For instance, in hypothesis testing the null hypothesis is proposed by the researcher as the opposite of what their hypothesis is. The null hypothesis is either rejected (which means the hypothesis is supported) or is not rejected. The null hypothesis is essentially a statement about falsifiability.