What did Baudelaire mean when he wrote that modernity refers to the ephemeral, the fugitive, or the contingent?

The full quotation to which you are referring is taken from Charles Baudelaire's "The Painter of Modern Life." It reads:

By ‘modernity’ I mean the ephemeral, the fugitive, the contingent, the half of art whose other half is the eternal and immutable…

The statement describes the work of Constantin Guys, who is referenced in Baudelaire's essay simply as "Monsieur G." Guys (December 3, 1802 – December 13, 1892) was a journalist and illustrator best known for his...

The full quotation to which you are referring is taken from Charles Baudelaire's "The Painter of Modern Life." It reads:

By ‘modernity’ I mean the ephemeral, the fugitive, the contingent, the half of art whose other half is the eternal and immutable…

The statement describes the work of Constantin Guys, who is referenced in Baudelaire's essay simply as "Monsieur G." Guys (December 3, 1802 – December 13, 1892) was a journalist and illustrator best known for his reporting on the Crimean War. The essay, while overtly focusing on the work of Guys, also defends the work of Impressionist and Symbolist painters that Baudelaire admired.

In this essay, Baudelaire is arguing that "modern" art must move behind the classical ideals of grandeur and timelessness to capture the fleeting impressions of everyday life, even at its most squalid. Unlike the Naturalists, he is not arguing for realism so much as artistic vision, which he says is transformative, creating beauty from fleeting impressions. He is also arguing for casting off the straight jacket of artistic tradition and embracing the modern world, rather than imitating ancient models. 

Guys' work, in its simple technique and response to the details of immediate experience, represents Baudelaire's ideal of the flâneur, strolling through the city and observing its varied inhabitants.