As you begin to do so, you can keep a record of them in a spreadsheet or notebook. Look up their biological classifications. All of a sudden the classification system will start to make sense, and help you understand the diversity of the organisms around you.
Biology is one of those subjects where part of the context comes from being outdoors and trying to understand ecological relationships yourself. You don't have to get to the level of a pro biologist, but there is so much you can find out by experiencing nature and trying to understand the basics that anyone can do it.