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Awesome project man!!
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LDR senses the hit. For a better info try to go through the project once again.Though if you are asking how LDR works?Answer is that it changes its resistance when the light hits it,hence the name Light Dependent Resistor(LDR)
Its a difficult prospect to use it in bright light.as it depends on light to trigger the system.You can try out other methods to achieve the result for weapon training.But if you still wanna try this idea out in day light you could try to make laser pulse in a particular frequency and then use a decoder at the target end to detect if the same frequency of light is being hit on the ldr,for that to happen you would need some basic knowldege of logic gates and timer chips like 555 timer