Scientist have been measuring increasing levels of greenhouse gases in Earth's atmosphere. How do increasing levels affect the atmosphere?

Well, we have a book to write on this topic but imma explain it briefly plus simply.

Global warming emphasizes the environment with rising temperatures, water shortages, increased fire threats, droughts, weeds and pest attacks, severe storm damage and salt attacks, to name just a few.(In simple words)

Now, we'd go briefly and discuss some common affects briefly :

Hotter days - The climate is getting more and more warmer and year 2015 was the hottest year ever record throughout the history. The Earth's temperature had already warmed by 1°C which is really dangerous. Rising sea levels - Rising sea levels due to climate change is the biggest problem causing natural calamities. Increased ocean temperatures are melting glaciers and ice caps all over the world. Melted ice increases the volume of water in our oceans. Warmer temperatures also result in the expansion of the water's mass, which causes sea levels to rise, threatening islands and coastal cities.More frequent and intense extreme weather - Extreme weather events like bushfires, cyclones, droughts and floods are becoming more common and more aggressive as a result of global warming.

Hope it helps <3