The phrase to "not let our left hand know what our right hand is doing" is used by Jesus during the Sermon on the Mount in reference to our behavior in giving. In full, Matthew 6:3–4 states: "But when you give to the needy, do not let your left hand know what your right hand is doing, so that your giving may be in secret. And your Father who sees in secret will reward you." Clearly, this command from Jesus is not literal but focuses on the thoughts and intentions of our heart. Instead of giving to make ourselves look good or for others to see how “good” we are, we should always check the motivation behind our giving and give humbly and out of our love for the Lord.
Rather than being literal, when Jesus said not to let your left hand know what your right hand is doing, He was talking about what the condition of our hearts should be when we give. There were hypocritical people in Jesus' day who would give charitably to the poor and were very public about it. They wanted others to notice and recognize them for their generosity. In contrast, those who give "in secret," for the joy of giving rather than for the appearance of generosity or spirituality, will be rewarded by God. Those who want to show off what they have done already receive their reward by the praise people give. Instead of doing things for others so that people will think more highly of us, we should give because we love God and want to do good. He sees us, and how He views us is more important than the praise of people.
In Matthew 6, Jesus talks of keeping things secret between our left and right hands as an illustration of how confidential we should be with our giving, and, even more importantly, how humble the posture of our hearts should be. When we give to others without our left hand knowing what our right hand is doing, we are avoiding hypocrisy in our motivation and storing up eternal treasures. The focus in all of these acts is worshiping God, not making ourselves feel righteous or trumpeting our sense of holiness for others to applaud.
Does this mean that we should never tell anyone about our giving? Not really; there is no inherent hypocrisy in the act of giving. In general, it is wise to refrain from the temptation to be prideful that could come from making our generosity a public display. The primary thing that we need to keep in check is the motivation behind our giving. We should give from a place of loving the Lord and focusing on eternity instead of human praise and validation.