what is the source that every four amot (~2 meters) walked in Israel is a mitzva? (read this somewhere)
Also, what is the reason for this mitzva if it has any.
aish brings the sources
You shall possess the Land and dwell in it - Bamidbar 33:53
and the gemara in Ketubot 111a
Whoever walks four amot in the Land of Israel may rest assured that he will be a denizen of the World to Come
Ohr Somayach cites the Maharal explaining the reason
Because of the intrinsic Holiness of the Land of Israel, a person gains spiritual merit by merely walking here
See also aish for more details on the relevance of this mitzva today
The question, however, is whether this mitzvah is compulsory in our times when the Holy Temple is not standing. This is the basis of a dispute between two great Talmudic commentators, Maimonides and Nachmanides. A leading 20th century sage, Rabbi Moshe Feinstein, concludes that living in Israel is a "mitzvah kiyuma" – while it is a great mitzvah, there is no absolute obligation to do so.
See also here