Let's stick to 21st century knowledge, for starters.
Today, common ancestry of species is a genetic fact.
You can argue with this till the cows come home, but it is what it is. Phylogenetics demonstrate beyond any reasonable doubt that species in fact do share ancestry. It's pretty much as close to fact as you can get on that point. That, plus the fact, off course, that we have literally observed speciation events.
Evolution theory deals with the process of evolution. It's an explanatory model that attempts (very succesfully) at explaining the facts of biology. One of the facts it explains, is the genetic fact that species share ancestry.
"morphed" is also one of those words that only sows confusion and which isn't accurate.
To "morph" is something that an individual does. In evolution, that's not how it works. Creatures die as the same species that they were born. Neither do members of species X give birth to a member of species Y. It's a gradual process which works through the accumulation of micro-changes over generations.
As the saying goes: lot's of small fish, make up for a big whale.
In layman's terms, I'ld say something like this:
Evolution is the process of accumulation of micro-changes in a population, through genetic inheritance and filtered by a selection process, eventually leading to speciation events.
This simple statement can explain the entire tree of life, and the nested hierarchy it comes in.
It can also explain the fossil record, comparative anatomy, comparative genomics, geographic distribution of species, etc.
It has gigantic explanatory power.