I have old style fuse box, with main and range pull outs fused... I blew one side of main pull out... 60 amp... my question is why did some circuits, such as overhead lights still have voltage but probably low voltage... because the lights were dim... thanks...

If by chance you had any 240 volt appliances that were connected and working at the time, you could encounter back feeding.

If you blew only one side of the main, there was still voltage between the other side and the neutral.

In a 240/120 single phase install, the primary of the transformer feeding your residence is single phase. The secondary is 120-0-120 where the 0 tap becomes ground/neutral. Thus, between the 120 V taps you have 250 V, because these voltages are 180 deg out of phase.