Save is to keep or store something for some reasons.

Examples:

Since last year, i saved my money up to buy a new car.

去年我就开始存钱准备买车。

Those files should be saved in the computer in case we use them one day.

那些电子文件应该保存在电脑上，以备将来用得着。

Store is to put or leave something somewhere (a warehouse, or computer memory) for some time and will use them in future.

Store是储存储藏的意思。多用于现实存在的东西的存储，比如商店仓库货物存储。以备将来使用。

Example:

I stored my winter clothes in the bags.

我把冬装存进了袋子里。

My mom stored my old clothes in one special room.

我妈妈把我的旧衣服存到了一个专门的房间里。

Keep is to not throw away something.

Keep是存放保留的意思。强调的是不丢弃、不放弃。

Examples:

The girl started to keep her hair long time ago.

那个姑娘很久之前就开始留发。

The boy keeps his toys although he rarely plays them any more.

那个男孩一直保留自己的玩具，尽管他很少再拿出来玩。