When you want to connect SharePoint Online remote site using CSOM, ClientContext object to be initialized with the Web URL.

The new SharePointOnlineCredentials class has been introduced by CSOM for SharePoint 2013 which provides this functionality.

// Namespaces
using System;
using System.Security;
using Microsoft.SharePoint.Client;

// String Variable to store the siteURL
string webUrl = "http://target.sharepoint.com";
// String Variable to store the user name
string userName = "name@tenant.onmicrosoft.com";
// String Variable to store the password
string password = "xxxxxxxxxx";

SecureString securePassword = new SecureString();
foreach (char ch in password)
  securePassword.AppendChar(ch);


using (ClientContext context = new ClientContext(webUrl))
{
  context.Credentials = new SharePointOnlineCredentials(userName,password);
  // To retrieve the web's title.
  context.Load(context.Web, w => w.Title);
  // Execute the query to the server.
  context.ExecuteQuery();
}

Supply the URL, username, and password of a user that has permission to access the site using CSOM.