Ceiling junction box daisy chain

I’m doing a bathroom remodel in my house which has old wiring. I capped the light switch and took down the light fixture the find three sets of wires. The power comes into the box the cable for the switch comes down and then the last cable carries onto to bedroom outlets. I’m curious as to why there’s a white wire with the blacks and if I can wire another recessed light into this box. My electrical knowledge is very basic. Thanks in advance