Look at this picture, the yellow line is the laser in question.
A laser is made of light, moves at lightspeed, and stays uniformed for a time. The yellow line in the middle shows how the entire line moves at the same speed, both the "tail" and the "head" of the laser move at LS because it is light.
Now the bottom one shows what happens when light hits a surface, it is both reflected off of and absorb by that surface. The line is now shorter because part of that laser has been reflected and absorbed by the red line. However the tail of that laser has not yet hit that surface, which in this case is Star.
Star was hit by the head of the laser, and as light it's both reflected and is absorbed by her. However before the tail could reach her, she activates her Quirk which makes a rule that allows her to hold light. You can see the tail of the laser bending after she grabs it, she changed how the light works it appears to have turn solid.
The light is now bending it's all scrunched up as the laser gets squished, think of the laser becoming rubber at that moment. Honestly I think she changed the property of the laser itself, instead of letting her hold light. She needs to say something's name in order to affect it, she doesn't say her name when the laser hits her. Instead she says laser, and now she can hold it.