(someone) can tell (clause)

When you "can tell" something, it means that you know it based on something you saw:

I can tell that you're lying to me.

Could you tell I wanted to leave?

You can leave "that" out in casual conversation, but in formal speaking or in writing you should definitely include it:

I can definitely tell that you're improving.

Use "___ can tell ___" to talk about things that someone noticed out on their own. Don't use if for things that someone heard from other people. In that situation use a phrase like "I heard ___":

I heard you and Desmond weren't getting along.

definitely (do something)

When you use "definitely", it means that you're sure. You use it to show how strongly you feel:

 I definitely want to go.

"Definitely" is often used together with "can tell":

I can definitely tell that you've lost some weight.

You use "definitely" before a verb, but you can also use it before an adjective:

I'm definitely taller than him. He's like two inches shorter than me.

(be) getting better

When you're "getting better", it means you're improving:

I'm getting better, slowly but surely.

"Get better" is a more casual version of "improve".

"Get better" also means to recover after a sickness or injury, by the way.