Direct measurements are ones you actually take with gauges or Instruments or by counting. You could use a rain Gauge and record rain fall or you could measure the amount of carbon dioxide in air..

Indirect measurements are taken of something other than the actual thing of interest. For example, the rings of a tree might indicate that ten or twenty years ago there was less rain because the rings are narrower. The amount of carbon dioxide trapped in polar ice-caps might be used to estimate the concentration of CO-2 in the air.

A direct measurement would be counting the number of people who walk through a stadium gate and an indirect measurement of this would be counting the number of tickets sold or counting the money from the sale of tickets. The two indirect measurements could be wrong because not everyone who buys a ticket uses it or the handling of the money was inappropriate.

Here is some text from Wikipeida about how CORE body temp (i.e. temp in middle of your body) is indirectly estimated by measuirng other body areas:
It is claimed that changes in core body temperature are reflected sooner and more accurately in the ear than at other sites. Whilst the electronic display of the temperature value is easier to read than interpreting the graduation marks on a thermometer, there are some concerns for the accuracy of ear thermometers in home use[1].

Influencing factors on other areas where temperatures are taken:

Oral temperatures are influenced by drinking, eating and breathing.
Rectal temperatures lag behind changes in core body temperature and there is a risk of cross-contamination.
Skin temperatures, measured under the arm or at the forehead, are not always reliable indicators of core body temperature, especially during those critical times when core body temperature is increasing or decreasing. This is because the skin is a tool the body uses to control core body temperature. For example, when fever is increasing people are likely to react by shivering and drawing in heat from the increase core body temperature. Skin temperatures are further influenced by factors such as fever lowering medication, clothing and external temperature.