It has an interesting application in real life.
Forensics experts use Newton's Law of Cooling to find out when victims of crimes died. They take the temperature of the body when they find it, and by knowing that the average temperature of the human body is 98.6 degrees initially (assuming the dead person wasn't sick!) and measuring the room temperature, they can find k and then find t.
There are several other applications which make it significant.
Hope it answers your question.
All the best!