When we remember something, our brain is accessing a specific part of itself that it uses to store memories. If the brain is damaged, sometimes the pathway to the memory portion of the brain is disrupted or the memory portion itself is damaged. Both of these lead to the brain no longer being able to access the memories.

Our brains are made up of over 100 billion cells called neurons which pass information between themselves and process all the information we take in through our senses. These neurons are separated into brain regions, which all handle different things. For example, you have a visual area that processes your vision and a separate area that stores memories.

These neurons communicate by passing signals between themselves using certain chemicals (neurotransmitters). When the brain is functioning normally and wants to remember something, the brain region that stores memories recalls the memory and sends it to the rest of the brain through some connecting neurons. If these connecting neurons get damaged or the region storing the memory is destroyed, the memory region cannot communicate the remembered things with the rest of the brain anymore and the memory is lost.

Imagine the brain as a library. Each part of the library has a different purpose and stores different kinds of books, just like each portion of the brain does different things. You have a section on different languages (language region of the brain), on sports (motor area that controls all movements), history (the memory regions), and many more.

In a normally functioning brain, you can go to all parts of the library, so when you remember something you walk to the history section and pull out the book you want. If the hallway to the history section (the pathway to the memory section) is destroyed, you can no longer go there and the memories are lost. If the history section itself is destroyed (the memory region is damaged), you can go there but the books are destroyed, so the memories are lost.

In short, the reason people forget things after receiving brain damage is that region storing memories is either damaged or can no longer communicate with the rest of the brain.

Your question is great because it includes an element of how scientists explore memory.

Scientists study people with severe brain damage to help them, but also to learn about how the brain works. By comparing people with injuries in different parts of the brain, scientists have figured out which parts of the brain are uniquely responsible for our different abilities. We have discovered that there are many different types of memory. For instance a memory of what you had for lunch yesterday (and where you were, who you were with) is called an episodic memory. By studying the brain damage of people with amnesia, or the inability to remember these sorts of things, scientists have determined that a part of the brain called the hippocampus is responsible for episodic memories. So if an accident or disease damages this part of the brain, people can lose their ability to recall past events and make any new memories about events in their lives.

However there are other types of memories that remain unaffected even if the hippocampus is damaged. For example your knowledge of how to tie your shoes or how to ride a bike is called a procedural memory. It turns out that memories like this are handled by different part of the brain. In fact amnesiacs who cannot remember a single day of their life can still learn new skills, like getting better at solving puzzles, without being able to remember ever doing a puzzle. So depending on where brain damage happens, one may lose different abilities, but keep others.

One of the brain's functions is information storage. Damage the brain, lose the information contained in it. Since your memories are information, damaging your brain may cause you to forget them.