apne here means family member or someone close as close as that.
"Apno ko jab apne kho dete hain,
when people close to use lose someone close to them,
Tanhaiyon mein wo ro dete hain,
they cry/mourn in loneliness,
Jinko hamne apni palkon par baithaya hai,
(palkon par bithana literally means placing someone on the eyelids, which means adoring and cosidering someone highly special)
those, whom we have adored so much,
Wahi in palkon ko aksar bhigo dete hai" (palakein bhigona, wetting eyelids/eyes)
often they only hurt us.