A lagging indicator is an indicator that lags behind the price action or the broader economy. In other words, it registers change after that change has been felt in other areas of the economy.
Lagging indicators exist in both technical and fundamental analysis. Moving average crosses are an example of a lagging technical indicator.
MA crosses lag the price action because for them to be able to register the change it has to have already taken place. This is why traders use them to confirm trends that are already underway.
A good example of an economic indicator that lags the broader economy is employment. This is because for there to be an increase or a decrease in available jobs, other factors must have already come into play in the economy at large.