control flow elements (of which at least one is required in a package and which consists of one or more tasks and containers which are executed when the package runs).
data flow elements (which consists of data sources and destinations)
event handlers (a workflow that is triggered by packages, tasks or containers when certain events occur)
variables
parameters
configurations (property-value pairs)
A package can be created with a graphical tool or programmatically.
The two graphical tools are
SSIS Designer
SQL Server Import and Export wizard
Packages are stored either
in SQL Server,
the SSIS Package Store or
in the file system
Multiple packages can be put into a project which then can be deployed as a unit (see .ispac files)
Packages can be configured and executed with DTExec.exe.
Designer
An installation of SSIS does not come with the tools with which SSIS packages can be designed and developed.
This is probably the reason why there is also SSIS Designer.
SSIS Designer is a graphical tool to create and maintain «SSIS packages». In particular, it allows to
construct a package's control flow
constract a package's data flows
adding event handlers to the package and the package objects
This Youtube movie, which I found later, indicates that its also possible to install integration services for Visual Studio from Visual Studio via its «marketplace».