Mr. Maru: Ok, you need to feed the fish, wash the dishes, and vacuum the living room.
Sparky: Understood.
Mr. Maru: um, OK. Oh, we need to do the laundry before 4!
Sparky: I understand.
Mr. Maru: … Right. You're a little strange today Sparky. To do the laundry, you need to push the red button then kick the machine once, OK?
Sparky: Gotcha.

How can say you know the meaning of something? There are several options: Gotcha, I understand, understood, or got it.

Let's start with the most formal first:

Understood.

This can and does sound very formal. It is like a robot. This is usually used when a person with power talks to someone below them and the speaker is a little disappointed.

Boss: We don't have the money for the project. We have to shut it down.
Employee: Understood. (He is disappointed.)

Next is 'I understand.' This is a little formal and has several uses. It is usually used for emotional situations. It can sometimes mean 'I know the way you are feeling.'

Boyfriend: I'm sorry I got angry. I was in a bad mood.
Girlfriend: I understand.

Friend A: I can't go to your birthday party. I'm too sick.
Friend B: I understand. Take care!

Then, we have 'Got it.' This usually means 'I know the way of doing this task.' It is a little casual or informal, but can be used in business situations.

(learning to drive a manual transmission car)
Father: To shift into first gear, put your foot on the clutch and move the gear from neutral to first.
Son: Got it! (Grinding sound)

Teacher: To make the /l/ sound, you need to put your tongue forward, close to your lips.
Student: Got it!

There is one last informal casual phrase to use:

Gotcha.

They all mean 'I know the meaning of something.' It is a social English phrase.  It should be used in light situations.

Roommate A: Don't open the basement door. The cat is down there.
Roommate B: Gotcha.

Now, it's your turn, can you correct Mr. Maru's and Sparky's dialog?  Try it in the comments below.
Or teachers, can you think of other ways to say 'I know the meaning of something?'  Let me know in the comments.