Understand: learning at the coffee shop

• verb ‘realize’ is often used for talking about the state of understanding and knowing things: I realize this is difficult for you. It is also used to say that we start tounderstand something: As she was speaking I suddenly realized that we’d met before.
• In British English, the phrase ‘the penny drops’ is used to say that you or someone else finally understand what is being said or what is happening: Then I saw them together at Sophie’s party and the penny dropped. I had no idea that they were a couple!
• verb ‘grasp’ also means ‘to succeed in understanding something’ and is often used to talk about understanding difficult things: It was quite a high-level talk but I think I managed to grasp the main points./She couldn’t seem to grasp the concept. (The noun ‘grasp’ is also used: His grasp of grammar is very impressive for a seven-year-old.)
• A phrase which is used for succeeding in understanding is ‘get the gist’.  I think I got the gist of what he was saying.
• Another such phrase is make sense of. I’ve read the paragraph three times now and I still can’t make sense of it!
• If you appreciate something serious about a situation, you understand it or you understand the reasons for it:I appreciate that this is a very difficult decision for you to make.
• ‘comprehend’ is a formal near-synonym for ‘understand’. We comprehend serious, difficult things, situations rather than subjects: They evidently failed to comprehend the seriousness of the threat.
• Similarly, you might say ‘I get the picture’ to a person who is describing a situation in a slightly indirect way to let them know that you understand what they are saying: ‘He’s not the most organised person and he can be a bit forgetful.’ ‘I get the picture. I’ve worked with people like that.’