We are intending to be on display for Christ, rather than on stage for him.
When you go to an art museum, there are various works on display. None of them are shouting at you for your attention, none of them are clamoring for the best spot for display, and they do not speak a word to promote their own glory. They are silent, but at the same time plainly testify to something outside of themselves. Some are contemplative, others are beautiful, quirky, amusing, or even gaudy. But they are unaware of themselves in a wonderful way - simply 'being' what their maker made them... Reflecting the artists skill and personality which brought them into being.
An actor, on the other hand, consciously puts on a different face in every play. The person who appears when the lights may be loud and blaring even though the actor may be quiet and meek. Actors toil at their craft, and no doubt take pride in it. Most walk on stage thirsting for the applause and adulation of the curtain call. They gleefully sign autographs or grant interviews to reporters and critics who want to know them and their gifting. Playwrights write plays for them - having a particular person in mind for a particular role.
They must perform and be noticed, because their next role depends on them being valued and known. Far too often, the craving for attention spills over into a life that can no longer distinguish between the private and the public - never being able to escape the stage. Sure, they point to the mastery of the playwright (to the degree their acting allows them to 'disappear' into the plot), but they are not unconscious of it.
So, it shouldn't be surprising that the word for 'hypocrite' in our passage is the same word for an actor. The hypocrites were out to display themselves and their faux righteousness, stepping on stage and calling all eyes to rest on them. Whatever attention went to God for their giving, prayers, and fasting was secondary to them - a fortunate side-effect of their curtain call and evidence of God's grace surpassing our sin.
We must live our lives before God, humbly willing to take no credit and receive no praises while here on Earth. This doesn't mean we don't talk about our giving or pray in public ever... However, we must have hearts that are content with the Savior alone seeing our lives and being pleased.
Calvin, commenting on these verses puts it so well:
[Jesus] tells them, that God does not need a strong light to perceive good actions: for those things, which appear to be buried in darkness, are open to his view. We have no reason, therefore, to suppose that what escapes the notice, and receives not the testimony of men, is lost... A most appropriate remedy is thus applied for curing the disease of ambition, when he reminds us to fix our eye on God: for this banishes from our minds, and will utterly destroy, all vain-glory. — In the second clause, which immediately follows, Christ reminds us that, in looking for the reward of good works, we must wait patiently till the last day, the day of resurrection. Thy Father, says he, shall reward thee openly.
To express it in a few words, whether a man prays alone, or in the presence of others, he ought to have the same feelings, as if he were shut up in his closet, and had no other witness but God.
Believers do not pray, with the view of informing God about things unknown to him, or of exciting him to do his duty, or of urging him as though he were reluctant. On the contrary, [believers] pray, in order that they may arouse themselves to seek him, that they may exercise their faith in meditating on his promises, that they may relieve themselves from their anxieties by pouring them into his bosom; in a word, that they may declare that from Him alone they hope and expect, both for themselves and for others, all good things. God himself, on the other hand, has purposed freely, and without being asked, to bestow blessings upon us; but he promises that he will grant them to our prayers. We must, therefore, maintain both of these truths, that He freely anticipates our wishes, and yet that we obtain by prayer what we ask.
May God display His beauty and perfections in us, and remove all our ambition for the spotlight and the encores of the crowd.