Spirituality.

What do people mean when they say, "I'm not religious but I'm spiritual"?

I believe they are stating, like the hippies of the 1960s and 1970s, that they do not subscribe to the moralistic, sex-phobic, hypocritical Christology of the western Churches.  The fear-guilt manipulation of the conservative establishment.
But they do believe in God and they do agree with most of Jesus' teachings of forgiveness and compassion.

Their image of God, and indeed of Jesus, is quite different from the orthodox traditional images: the angry, harsh, judgmental God and the Lamb without spot who became a human blood sacrifice to take away the sins of the world, which were inherited from Adam and Eve.
They don't believe we are fallen and in need of redemption.  To them this is pure Machiavellian manipulation.

So what do they mean when they say that they are spiritual?

I believe they mean that they are idealistic.
These are the non-materialistic ideals of the hippies: equality, non-violence, socialism, compassion, forgiveness, a healthy attitude to the body and sexuality, and the redistribution of wealth.
This is combined with green values of preservation and protection of the environment: the great cathedral of nature.

This vaguely connects with God as a benevolent, creative force.  And Jesus as a spiritual teacher rather than a dying deity.

So this fits perfectly with Progressive Christianity: original blessing, a benevolent God, the historical Jesus, social  justice, and ecology.

But Church!?