What does the maxim paintings and fightings are best seen at a distance mean?

This phrase refers to multiple specific truths:

A painting, when viewed closely, has errors, is essentially a series of globs and irrational lines, shows little logical sense, and generally appears to be aesthetically displeasing. When standing at a distance from it however, the painting's overall picture can be seen more clearly and small blemishes and irrational structures in the painting are not as readily apparent.

For this reason, art should be viewed from a distance.

"Fightings" or probably more accurately, "Battles" should be viewed from a distance because if one is close to a battle, they are likely also part of the battle, which means their life is in jeopardy.

The phrase when put together is meant to communicate a witty message about how being too close to something makes it unappealing.

It can also be inferred that the person originally making this statement was critiquing human nature and the fact that when looking back historically or when seeing images or imagining battles in our minds, we as people see them as glorious, interesting, and entertaining events.

Actually being in a battle however, is a gruesome, disgusting, horrifying experience that is contrary to every sense of humanity that most of us are given as instinct.

It is likely a critique on human nature and how people tend to view war and conflict with fascination and intrigue, and might even encourage the event or find it entertaining; so long as that person is not specifically part of the battle itself.