Most people have a tendency to not think about what goes down their drain until a sink or shower clogs. They will leave things in the sink that will eventually, but shouldn't, go down the drain. The same applies for a shower drain. Think about how much hair ends up on your shower floor in the course of a week: Especially, if multiple people are using the one shower. When drains backup, it can ruin the flow of things in a house. It can stop kitchen and bathroom activity, and that is always an inconvenience. There are a few things that you can do preemptively so that potential issues in the future don't arise.
Do not put cooking grease down your drain. Instead, place it in some tin can that will later be disposed of in the garbage. If you have an old coffee tin, cat/dog food cans, or soda can (these are harder to use with the opening, but the top of the can be cut off carefully) you can put the grease in there. Let it sit for several hours and then you can toss it in the trash. The reason to not do this lies in the chemical reactions that happen when flushing the grease. Once the grease is introduced into the sewer system it meets oils and chemicals from your kitchen. This can cause a bad build up in your pipes. Not only can these cause problems in your own home, but it can also lead to serious problems in an apartment building or community. This happens when individual plumbing runs into communal plumbing. It is easy to not have this problem happen to you if you simply keep your grease out of your drains.
The same applies for your coffee grounds. Some people would empty grounds into their sink before tossing filters. Although this wasn't such a problem ten years ago, it is becoming something more common with single serving coffee machines. Machines that have reusable pods need to be cleaned. It is very easy to clean them in the sink with water, but it isn't the best place to do it. Consider how the grounds can get stuck in the pipe, which will lead to future backups. Coffee grounds can be just as bad as grease, and so you should dispose of it in the garbage. Take some time to dispose of it properly and your system will run smoother.