External and internal validity are exceptionally important in psychology as they can show how generalizable the results of a psychological study are. When assessing results researchers should always use validity methods, as they, for example can then say whether their results are generalizable to the real world, and thus could improve everyday life.
External Validity consists of two main parts, population and ecological validity. Population validity is whether the results of a study can be generalised from the sample to the target population. So basically does the sample represent the people the study was aimed at. For example if a researchers study is too asses the motivation of Liverpool Football Club players, and the researcher had 50 Liverpool Football Club players of a range of ages and backgrounds, then you could argue that this study has a high population validity as his sample is very representative of his target population. On the other hand ecological validity is whether the results can be generalised into a real life setting. For example when a lab experiment is used, as the study is in an artificial setting, I would argue that the study has a low ecological validity and it is unclear the participants would act the same as they do in an articficial setting as they would in a natural setting.
Internal Validity is another useful tool for a researcher to assess his results. In simple terms Internal Validity means that if internal validity is considered as high then the researcher is measuring what he claims to be measuring. For example if the researcher is using a self-report measure and collecting subjective data about an embarrassing subject, then due to demand characteristics the participant might give false answers and thus the research has invalid research because he is therefore not measuring what he is claiming to measure. Maguire et al (2000) used an MRI scanner to measure the size of the anterior and posterior hippocampi located in the medial temporal lobe of the brain. Maguire wanted to measure the plasticity of the brain in regards to the memory of taxi drivers in London. As he was using an objective measure (MRI scanner) there is no way that Maguire was not measuring what he claimed to be measuring therefore his study would have a high internal validity.
As for the argument as to which validity is more important, personally I would say that Internal validity is much more important as if a researcher is not measuring what he thinks he is measuring then all his results are invalid and the study’s conclusions will not have sufficient evidence to back them up. Without a high internal validity, assessing the external validity is pointless as the results of the study are invalid anyway. However I can see how some people would argue that external validity is more important as they would argue that a study’s results are pointless if they cannot be applied to the real world, which is true and I also believe this. But as I have just stated if a study does not have a high internal validity then the results are corrupt and generalising corrupt results to the real world is pointless and would have a positive effect upon everyday life.
psueef 
I would argue that both internal and external validity are just as important as each other as both need to be high for the study to be considered useful. If either internal or external validity becomes low in a study, then the validity of the study as a whole is seen as lower. Therefore, to place a greater importance on one of these types of validity could corrupt the results of the study, because if one of the validity types is focused on more, then the other type becomes less of a priority. This would make it easy for the researcher to neglect one aspect of validity, reducing the validity as a whole, counteracting the extra attention paid to what they consider the more important part of validity.