つつある says that a change is under way: something is gradually getting better, worse, bigger or rarer. It goes after the ます-stem of a verb of change – ふえる増える, へる減る, かわる変わる, かいふく回復する – and belongs to writing: news, reports, essays.
A verb for an ordinary activity, such as eating or reading, does not take つつある: ×本を読みつつある. That is just 読んでいる.
With a verb of change, 〜ている usually gives the state the change has already produced. つつある puts you in the middle of the change, before it is complete.
The same goes for a change that happens in one moment: つつある describes the approach to it.
In conversation the same idea is きごう〜てきている or きごう〜ていく: you'd write 変わりつつある in a report and say 変わってきている to a friend.
つつある is a separate pattern from つつ, "while doing", which joins two actions.