Hi Sainath,

If your browser's popup blocker settings are configured for maximum security, you won't be able to view any popup windows within Salesforce. This includes all popup windows, even those that provide necessary functionality such as the calendar pop-up for choosing a date on an activity, confirmations prior to saving or deleting, lookup dialogs for selecting a record, the Help & Training window, and more.

To allow pop-up windows for Salesforce, add salesforce.com as a trusted site within your browser's popup blocker settings.
Add Wild Cards for sites that pop-up from Salesforce
*.salesforce.com
*.force.com
*.content.force.com
*.staticforce.com
Your browser may prompt you when a pop-up attempts to populate.  When this takes place, click Allow Pop-ups From This Site.

Otherwise follow the instructions below to add the domains above so that you will receive pop-ups from Salesforce.
Mozilla Firefox
1. Click on the menu button in the upper right.
2. Click Options, and scroll down to the Permissions heading. 
3. If "Block pop-up windows" is ticked, click on the Exceptions button.
4. Type salesforce.com in the "Address of website:" field, click on Allow, then click Save Changes. 
5. Restart Mozilla Firefox 
Google Chrome
1. Click the Chrome menu on the browser toolbar. Select Settings.
2. Click the Advanced menu on the left hand area of the browser window.
3. Select the Privacy and Security section. Click the Site Settings option.
4. Click Pop-ups and redirects. 
5. Toggle the selector for any site you want to Block or remove from the allowed list. Or use the Add option to add sites to the allowed list.
 
Safari for Mac
1. Click Safari | Preferences
2. Click on Security
3. Click on Websites
4. Locate the website URL in the list, then click the dropdown selection menu next to that URL and choose "Allow".
Some browser add-ons, like the Google toolbar, also have popup blocking. Consult your software documentation on those products for details on how to configure them to allow popups from Salesforce.

NOTE: A pop-up isn't generated if a due date isn't selected for the activity. If all browser issues are ruled out this might potentially be the issue.

Please mark it as Best Answer so that it can help others in the future.

Regards,

Priya Ranjan