'Guts' refer to the intestines of a person or an animal so to get to the guts of something means to get to the centre or the main gritty part of an issue or problem. This is an idiomatic expression used more often in informal situations.

1. My boss has a reputation for being rude, but I don't think she is. She just likes to get to the guts of a matter quickly rather than wasting time faffing around.
2. I'm too busy to listen to a long explanation about what went wrong in the negotiation. Please stop beating around the bush and just give me the guts of the problem. 
3. What I have just explained to you is the guts of how the computer system works in the office. You will pick up the rest as you go along.

1. Maybe if we sit down and talk we can get to the guts of what is bothering you.
2. I have the guts of €10,000 saved and I'm wondering how best to invest it.