The purpose of our existence in the eyes of the Ramban:[1]
The intent of all the Mitzvos is to believe in G-d and give thanks to Him for creating us. This is the entire purpose of creation, as there is no other reason for the original creation. The only desire that G-d has in the lower beings is that man know G-d and give thanks to Him for creating him. This is the purpose of prayer, and the communal services that take place in Shul; in order to have a set area to give praise to G-d for creating them, and to publicize this matter that we are His creations.
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[1] Ramban Al Hatorah end of Parshas Bo