If you take an area without forest and plant a forest on it then when the tree dies a new one grows in its place. A mature forest is roughly carbon neutral but reflorestation is taking a bunch of carbon from the atmosphere and converting it to tree trunks.

Does that mean that the Amazon rainforest is carbon neutral?

It was a major carbon sink, but as the climate warms up trees die earlier and release more carbon so it's becoming a carbon emitter. It's obviously hard to calculate an exact plus or minus, but it's not looking good, especially with the amount of deforestation occurring.

For now, the biggest contribution of the amazon rainforest in terms of climate is improving rainfall. If you cut down all that trees that regious would pretty quickly turn into a big desert (in fact, the forest is actually recent in geological terms)

Most green things add to topsoil which has to be heavily carbon. E.g., from my experience growing up, a healthy front lawn can add ballpark one inch of topsoil in 15 years. Similarly for prairies and forests.

Also a major fraction of trees, ballpark 50+%, have leaves and drop them once a year, and the leaves contribute to topsoil.

Even if a forest burns, the burned trees create ash which has carbon and adds to topsoil.

Some of the topsoil gets washed into rivers and lakes, becomes mud, gets covered over by more mud, and, thus, essentially buries its carbon.

There is more that is similar: a major fraction of the surface of the earth has, within 1000 feet deep, a lot of limestone, and that is partly, largely, or mostly just old sea shells where the animals pulled carbon from the water or what it ate and converted it to calcium carbonate, that is, buried the carbon (disclaimer, I'm no geologist).

In simple terms, basically, net, the earth's biosphere grabs and buries a lot of carbon including CO2 from the atmosphere.

Note: Nowhere here have I made a remark of any kind about the effects on climate of CO2 in the atmosphere.