what does it mean of when the going's tough?

In this context "going's" is in reference to the current series of events.

For example, if we were to hike up a particularly hard route, you could say, "Wow, the going's tough."

Mostly popularised by the song by Billy Ocean - When the going gets tough, the tough get going.

Using a play on the two separate meanings of each of these.

The first being, when one encounters a series of difficulties. The second being, the tough individuals then get moving to solve these difficulties.

Yes, "when the going is tough."

Use this definition of "going"

2.2 Conditions for, or progress in, an endeavour.
Lexico

Perhaps the "endeavor" meant in that song is the relationship between the singer and the person addressed by the singer.