In chemistry, a pure substance is a single element or compound that is not mixed with any other substance. This is stricter than the everyday meaning. In shops, pure milk means milk with nothing added, but milk is still a mixture of many different substances, so in chemistry it is not pure.
Pure elements and compounds melt and boil at specific temperatures. For example, pure water melts at 0 °C and boils at 100 °C, and it does so sharply at those exact temperatures.
A mixture behaves differently. An impure sample melts gradually over a range of temperatures, and it also boils over a range. This lets us use melting point and boiling point data to tell a pure substance from a mixture. We measure the melting point of a sample and compare it with the data book value. If it melts sharply at the data book temperature, the sample is probably pure. If it melts over a range, or well away from that value, it is impure.