I often hear "ели ели" but I haven't still had a clear meaning of that phrase. What does it mean? (Obviously, I'm not talking about "eat eat"). :)
As stated in the comments and answers, the phrase I meant was ""еле-еле" and not "ели ели" .
Most probably you misheard "еле-еле" which means "with great difficulty", "scarcely".
Он еле-еле идет.
He's barely even walking.
Without the context, it's hard to tell for sure, though. There are other, less probable, options:
Мы ели, ели, ели и, наконец, все съели.
We ate and ate and ate until there's nothing left to eat.
Одержимые новогодние ели ели празднующих.
Possessed christmas trees ate people enjoying the holidays.
Полуживые от голода посреди Сибири они ели ели.
Half-dead from hunger in the middle of Siberia, they ate fir-trees.
Детсадовцы еле ели кашу с комочками.
Kindergarteners were barely able to eat a porridge with lumps.
Sometimes, people choose to emphasize "е" sound at the end of "еле", but most of the times pronunciation in each of these cases is absolutely the same. You'll need to figure it out from context. Less likely options almost never occur in the real-life conversation between adequate adults.
It is something in between "like a tardigrade" and "struggle to" or "barely".
She struggled to learn the poem by heart. Она еле-еле выучила стих наизусть.
Мы еле убежали от копов. The cops barely got us busted.
He is barely breathing. Он еле дышит.
Мы еле затащили елку в дом. We struggled to drag the Christmas tree into the house.
Еле-еле душа в теле.