It directly means to leave someone. But of course, God didn’t literally leave anyone. Nor is this an indication that God isn’t Christ. It is, instead, a cry of pain that we all experience under the worst conditions. And more than that, a questioning of the true benevolence of God. After all, what all Good God would leave you in your sorrow? Why wouldn’t he lift you? Christ’s words are an exact mirroring of that sentiment, but what makes it spectacular is that he himself is God the son. What this communicates, therefore, is that the burden of life and suffering and sin, pushed to their furthest extreme, bring all - including God himself - understandably to such a point that we cannot comprehend how it could possibly serve the good.
All that to say, it isn’t a statement of God literally not being present at the cross, but rather a statement of the intensity of sin and evil and suffering to even bring God himself to doubt his own benevolence.