TL;DR
“We, the People” means that the Constitution is adopted in the name of the people of India. It means that the power to govern comes from the people. We are not subjects of a ruler; we are citizens who have given ourselves this Constitution.
What it means
The Constitution does not begin with “The Government” or “The King.” It begins with “We, the People of India.” This was a deliberate choice. It says that the people are the source of authority. The government and all institutions get their power from the people, through the Constitution and the law.
Why it matters for us
When we say “we the people,” we remind ourselves that we are not helpless. We have rights. We have the right to vote, to speak, to ask the government for answers, and to approach the courts when our rights are violated. We also have duties — to respect the Constitution, the flag, and the nation, and to promote harmony. “We the people” means we are all in this together: one people, one Constitution.
In daily life
When we raise an issue with the government, when we file an RTI, when we sign a petition, or when we vote, we are acting as “we the people.” We are using the power that the Constitution gives us. We are not asking for a favour; we are exercising our right as citizens.
Related: Preamble of the Constitution (Simple Explanation), Introduction: Constitution for Citizens, Why Fundamental Duties Matter.