Electrical – DRC error in pcb designing

Change the font of the name to be 'Vector', not 'Proportional' - you can do this by smashing the component with the smash tool and then editing the text. Otherwise Eagle requires clearance around the text.

Alternatively, and especially in this case, you should move the C1 name label into the free space near the component so that it doesn't overlap the stop layers and importantly isn't partly covered by the IC outline otherwise readability is affected. Again this is done using the smash tool which allows the text to be moved separately from the component.

This is a clearance rule, specified as 10 thou (the default rule).

On layer I3 in the design, you have a pad overlapping a track or another pad by 6 thou (hence the -6 in the Actual clearance column). The pad in question is highlighted.

The rule highlights errors from different nets.

In this case, you appear to have connected the pad highlighted to a track to pin 7, but the ratsnest shows this should be connected to pin 4.