This is usually not fatal .. as the error message says 'Some' Index files failed to download. Follows the same with 404 package error. you can either ignore this or update repositories and PPAs.
Hit http://in.archive.ubuntu.com vivid-updates/main Translation-en
Hit http://in.archive.ubuntu.com vivid-updates/multiverse Translation-en
Hit http://in.archive.ubuntu.com vivid-updates/restricted Translation-en
Hit http://in.archive.ubuntu.com vivid-updates/universe Translation-en
Hit http://in.archive.ubuntu.com vivid-backports/main Sources
Hit http://in.archive.ubuntu.com vivid-backports/universe Sources
Hit http://in.archive.ubuntu.com vivid-backports/main i386 Packages
Hit http://in.archive.ubuntu.com vivid-backports/universe i386 Packages
Hit http://in.archive.ubuntu.com vivid-backports/main Translation-en
Hit http://in.archive.ubuntu.com vivid-backports/universe Translation-en
Hit http://ppa.launchpad.net vivid/main i386 Packages
Hit http://ppa.launchpad.net vivid/main Translation-en [154 B]
Err http://ppa.launchpad.net vivid/main i386 Packages
404 Not Found
Ign http://ppa.launchpad.net vivid/main Translation-en_IN
Ign http://ppa.launchpad.net vivid/main Translation-en
Err http://ppa.launchpad.net vivid/main i386 Packages
404 Not Found
Ign http://ppa.launchpad.net vivid/main Translation-en_IN
Ign http://ppa.launchpad.net vivid/main Translation-en
Err http://ppa.launchpad.net vivid/main i386 Packages
404 Not Found
Ign http://ppa.launchpad.net vivid/main Translation-en_IN
Ign http://ppa.launchpad.net vivid/main Translation-en
Err http://ppa.launchpad.net vivid/main i386 Packages
404 Not Found
Ign http://ppa.launchpad.net vivid/main Translation-en_IN
Ign http://ppa.launchpad.net vivid/main Translation-en
Fetched 59.6 kB in 29s (1,987 B/s)
W: Failed to fetch http://ppa.launchpad.net/ackondro/tibesti/ubuntu/dists/vivid/main/binary-i386/Packages 404 Not Found
W: Failed to fetch http://ppa.launchpad.net/tualatrix/ppa/ubuntu/dists/vivid/main/binary-i386/Packages 404 Not Found
W: Failed to fetch http://ppa.launchpad.net/upubuntu-com/office/ubuntu/dists/vivid/main/binary-i386/Packages 404 Not Found
W: Failed to fetch http://ppa.launchpad.net/vokoscreen-dev/vokoscreen/ubuntu/dists/vivid/main/binary-i386/Packages 404 Not Found
E: Some index files failed to download. They have been ignored, or old ones used instead.
The above are the last few lines ,when i run apt-get update in my system.
You need not worry unless it is causing troubles in particular issues (ex:installing some new applications , some file operations etc)
But if you want to be safe then you can try updating your repository source links. This is usually caused if you have outdated sources as your ubuntu repository links. So, updating repositories will solve this error.
Go through This for additional information about Ubuntu repositories.
Follow This link if you want to update repositories and PPAs for your version of ubuntu.
You can even update them by your Ubuntu update manager. How do I restore the default repositories? --follow this link to know how.