A rival is a person or group of people who are trying to do the same thing as someone else, and trying to do it better. They are "competing" against one another. Usually they are about equally good.
Competing in this way is called rivalry.
Two (or more) businesses may be rivals. For example: they may be selling ice creams in the same area.
Brothers and sisters may be rivals. For example: they may both be trying to get their mother's attention.
Countries may be rivals. For example: they may be trying to have power over the same thing. This can be a dangerous thing which, in some cases, can lead to war.
In sport, two teams may be rivals. This is a more friendly kind of rivalry.