A theme of Matthew chapter 6 is that we can only receive God's rewards by seeking God and his approval from the secret place in our heart. "Practicing our righteousness" for men to see will not result in the reward we truly need which is to receive the incredible gift Jesus gave as his life for us as payment for sin.
The chapter keeps reminding us those who seek approval and the notice of men will not be rewarded--IE given eternal life but will only receive the rewards men can give. Joshua the 6th book of the Bible is about crossing over the Jordan into the new land and six is symbolic of our finally deciding to accept God's plan of redemption, cross over the "River of Life--Jesus" to the new land. God goes ahead of us but we must make the decision and take the action to cross which involves turning from sin thus making sacrifices and going and fighting battles to remove strongholds of sin in our life. Then we can enter step seven of God's Redemption Plan in which God promises to shepherd us to becoming complete.
Matt 6:6 "But you, when you pray, go into your inner room, close your door and pray to your Father who is in secret, and your Father who sees what is done in secret will reward you. (NASB)
The Bible tells us we are judged by what the Holy Spirit reveals about our heart condition. Verse 6:6 uses the word "Secret" which might better be said as "inwardly" or from the heart. The reference to our inner rooms seems a reference such as go to our heart and soul and talk to god from there. The phrase "WHO IS IN SECRET" seems a reference to the Holy Spirit which is there dwelling in us and this presence of God in us will see our actions and thus will reward us (The HS is the part of God in us that speaks/reports to God on our behalf).
WILL REWARD YOU: Strong's defines the word used for reward as to Give something of one’s self to another or to pay off a debt or things promised under oath. Thus, this fits the chapter theme which is about seeking God alone for our reward which as he promised is the eternal life he gives to us as a gift paying off our debt for sin.
Of course, this does not mean not to do good things people can see, but that our reward can only come from an internal heartfelt relationship with God.
The closing verse tells us we need not worry about tomorrow if we do these things, but take care of today which is having a relationship with God. Once we have done that God considers us his children and as a faithful parent will lead us to becoming complete. Thus, no need to worry about tomorrow (IE Eternal Life) if we have taken care of these things today.