The phrase "to change the meaning" refers to altering or modifying the significance or interpretation of something. It means making a difference in how something is understood or perceived. Full definition
What do these industry changes mean for pharmaceutical sales reps? (medreps.com)
Climate change means more deadly heat waves, allergies, infectious diseases and, potentially, a breakdown in food supplies. (scientificamerican.com)
As you suggested above, changing the mean by a small amount massively increases the size of a tail, as you've shifted much more of the distribution up. (realclimate.org)