What is ArcGIS Online?

ArcGIS Online is a complete, cloud-based, collaborative content management system that lets organizations manage their geographic information in a secure and configurable environment. The platform provides an on-demand infrastructure for creating web maps, web-enabling your data, sharing your map, data, and applications, and managing content and multiple users from your organization. It includes basemaps, data for your maps, applications, configurable templates, and GIS tools and APIs for developers. Organizations purchase a subscription which allows them to configure and manage their own ArcGIS Online site and set of resources. A subscription includes organizational accounts for members of the organization. Personal accounts are available for individuals who want to access content shared by Esri and GIS users and create, store, and share maps, apps, and data.

What can you do with ArcGIS Online?

A subscription to ArcGIS Online allows organizations to manage their geospatial content in a secure environment, publish maps and data in Esri's secure cloud, configure their own ArcGIS Online website, and create maps and apps from APIs, templates, and tools. It also gives them resources to share and collaborate with its members and beyond the organization. Organizations can share their geospatial content and provide access to critical information while staying in control of their data.

Manage your organization's geospatial content in a secure environment

Through a subscription, you get flexible data storage capabilities and administrative controls for managing user roles and access levels. Administrators of the subscription can invite specific users or groups of users with already established logins used in the organization and monitor usage through an intuitive dashboard. You can share content through groups with members of your organization, keep it private, or make it public. You stay in control of your data, lower your infrastructure costs, and empower your users and customers with easy-to-use, web-enabled content.

Publish maps and data as hosted services in Esri's secure cloud

Organizations can publish their maps and data as web services on ArcGIS Online. Esri takes care of hosting the services and scaling to meet demand. Web, desktop, and mobile applications can access the hosted services from anywhere on the Internet if the publisher chooses to allow it. The services can be published directly from ArcGIS for Desktop or the ArcGIS.com website.

Source arcgis.com

How to define points in a python script

Here is a little script for you to start.

import geompy,random,math

nPts = 240
print "Creating %s points"%nPts
for i in range(nPts):
    x = random.random()
    y = random.random()
    z = random.random()
    v = geompy.MakeVertex(x, y, z)
    geompy.addToStudy(v, "Vertex_%d"%(i+1) )
print "Done"

print "Creating a spiral"
nbPeriods=2
period=1e-2
t=0
step=period/50
ptList = []
while (t<=2*math.pi*period):
    x=math.cos(2*math.pi*t/period)
    y=math.sin(2*math.pi*t/period)
    z=t*50
    t += step
    v = geompy.MakeVertex(x, y, z)
    geompy.addToStudy(v, "Helix_%f"%t )
    ptList.append(v)
polyline = geompy.MakePolyline(ptList)
interpol = geompy.MakeInterpol(ptList)
geompy.addToStudy(polyline, "polyline" )
geompy.addToStudy(interpol, "interpol" )
print "Done"

Here I create 240 points in the for loop. Those are random points but you can use this loop to read a file which contains your points.
Then I calculate the coordinates of points on a helix and I use them to create points. Finally I use those points to create a curve (well 2: a polyline and an interpolate).

Hope this will help you.