To send to a portion of your list rather than the full list you will first need to create one or more segments.
A segment is a filtered view within your list.
Once you have created some segments you can then select a segment when sending an email campaign.
Segments will work best if your list has custom fields that you can filter by. For example if your list contains school contacts you might have a "School type" custom field that specifies if the school is a primary or secondary school and create a segment that only includes secondary schools.
To create a segment navigate to Lists -> click on the list you wish to segment -> click on Segments.