Cartography junkie here. I'll defer to someone who can tell you about this exact map or the exact period etc, but in the mean time:

Those are windrose lines, also called rhumb lines. The idea is that, for any one line, you could follow that around the globe and it will always hit latitude or longitude lines at the same angle. They're straight in the sense of a straight line on a curved surface. Think of them like great circle routes that planes follow today. They were an incredibly common feature of old maps as they were an important navigation aid.

You'll notice in each case they line up with either a latitudinal or longitudinal line on the map. The red lines are rhumb lines centred on some coordinate. The brown lines are the latitude and longitude. The only real circle there is the compass rose in the centre, from which you'd calculate your direction.

You'll notice the lines are in different colours. This was somewhat standardised. The brown lines on your image are the 4 cardinal directions, plus the directions exactly between them (NW, NE, SE, SW). The green lines split those, and the red lines split those.

The idea is, knowing your position, you can determine from this network of rhumblines how to get to your desired destination. It tells you which direction on the compass you should be heading.

You'll see this on a most nautical maps from the period.