Hi. What does this mean?

Imply is kind of a hard concept to get down on paper, as it often involves a note of sarcasm. 

If I were to say to you:

Don't you have to be to home by suppertime?

I could be implying (or meaning without actually saying) that I was tired of you being at my house and I wanted you to leave, but since it would be rude to actually tell you to get out, I would say something like that to try to give you a hint that you are no longer wanted. 

- You are standing around; you must be finished for the day. Implies that that person could probably find something more to do if they have time to stand around. 

- You must have forgotten that I wanted to go with you. Implies that the driver was supposed to pick up the passenger and didn't. 

- You must really like the taste of garlic. Implies that there is too much garlic in the food for the speaker.

Implication can be a discreet way of expressing an idea. In the example given, it might have seemed rude to ask if you were lazy. To avoid insulting you, the person asked why you were idle in a more indirect way.

they mean the same thing you meant when you said "what they meant" (except the time aspect).  the intended idea behind the word is what the word "mean" generally declares (means).

Imply means to suggest an idea (meaning or conclusion) without stating it openly.  the listener has to do a bit of work, and interpret what the person is saying yet not actually physically stating.  The meaning is somewhat hidden, on purpose usually.  Obviously, the meaning is not well-hidden or the implication would not be easy to identify, or even realize that it was there.  That would not be implying, that would be obfuscation (burying the actual truth through confusion and excessive lack of clarity). 

So, a person can openly declare, imply, suggest, obfuscate, or deny, as a range of possible ways to reveal or discuss a "truth".

Imply has several synonyms including: allude, hint, indicate, infer, insinuate, intimate and suggest. When you ask someone out on a date you imply that you like them. To imply is to use a less direct method of informing someone of they ought to think about doing. Say someone doesn't wash; give them soap as a birthday present.

Something here means using words indirectly to accuse or suggest you or someone or some thing. Using words in a roundabout way rather than directly saying what they'd really like to say, but rather hinting instead of being forthright or straight to the point. Rather than directly accusing, they'll imply. For example, if someone has bad breath, most people don't directly tell the person but rather hint to them by offering the person a mint. The person with bad breath will assume the other person was implying (hinting) they had bad breath. I hope I made sense with my explanation.