Using a field across several content type can be handy if a piece of data is relevant for several content types. A typical use case is a 'Phone number' field, used in both 'Restaurant' and 'Hotel' content types, even if hotels and restaurants are different enough to deserve their own specific set of fields and thus their own dedicated content types.

When a field has been added to more than one content type, we also say it is "shared", and that it as "several instances".

At the bottom of the Manage fields page for a content type, you'll find this:

In order to add a new instance of an existing field to a content type, you need to provide the following information:

Label

A human-readable name for the field. It will be used in input forms and on displayed content.
All characters are allowed, including spaces, accentuated or non-european characters.

Field:

The field to be shared.
A field cannot appear more than once in each content type. Thus, only fields that are not already present in the current content type will be proposed as "shareable". If none, the Add existing field option is not available on the Manage fields page for this content type.
Selecting a field automatically populates the Label and Widget values with the ones used by the previous field instance, but you can change them if needed before submitting the form.

Widget:

The form element that will be used to input data for this field on content forms : text input, select list, etc...
Each field type has its own list of available widgets. When selecting a field to share, the list of widgets you can select is automatically updated.