Actually, when you eat ingredients, one of two things happen: you get a message that the ingredient had no effect or an icon will show up in the bottom right corner. It's just that it's usually so fast that it's gone in the blink of an eye until your alchemy skill improves. You can see that something happened though if you go to your character screen and look at the bar for alchemy showing experience (not explaining it well) but if you hover your mouse over a skill, it shows what progression you've made so far.
The comment about identifying the effects that an ingredient delivers refers to when you hover your mouse over the icon of the ingredient in your inventory AND your alchemy skill is 15 or greater.
So even though your alchemy skill may be below 15, you can still figure out what its first effect is if you're quick enough - sometimes
You might find it useful to make a note to yourself until you build up your alchemy skill to 15+ so that you can stock up on beneficial ingredients because eating them does improve your skill over time. And if you want to speed things up, there are trainers out there,