Short answer: mass bends space-time; light follows space-time.
Longer answer: a property of mass-energy is that it bends space-time. Not only does this manifest as apparent attraction between objects with mass, but it also changes the path light follows relative to an observer’s point of view. From the light’s perspective, it propagates uniformly in all directions. But when direction itself bends, to another observer the light follows an apparently circuitous path.
EDIT 1: Wow! That blew up! Thanks for the awards everyone. I’m not a physicist, or even a science student, just an enthusiastic dilettante.
[Here’s](https://youtu.be/MTY1Kje0yLg) a cool video that helped gravity make more sense to me.
[Here’s](https://youtu.be/F5PfjsPdBzg) another awesome video that helps tie in the relationship between time and gravity.
And [another](https://www.youtube.com/watch?v=jlTVIMOix3I) video with a great visual analogy.
Just posting more [cool videos](https://www.youtube.com/c/pbsspacetime) as folks reply.
EDIT 2: Many replies which ask deeper questions about the subject exceed my capacity to offer what I feel are faithfully accurate answers. So if I don’t reply to your question, it’s because I’m not smart enough to offer what I feel is an edifying explanation.
Another great (https://youtu.be/XRr1kaXKBsU) shared in a reply below.
EDIT 3: Others have rightly pointed out that all energy (even light) bends space-time. But compared to mass (mass-energy), light’s effect on space-time curvature is minuscule (though light-only black holes are a thing! I never knew).
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