The Super Saiyan 7 is the seventh form of a Saiyan, this form is achieved upon extremely hard training for over 3 Years when on a power level able to go to the Super Saiyan 5. First achieved by Vegeta. Second achieved by goku.
The appearance of the Super Saiyan 7 is far different the Super Saiyan 6, as the fur and the near-SSJ4 characteristics disappear, returning to the previous series, the Super Saiyan 7 looks like the regular Super Saiyan, but with Dark Blue Hair instead of Golden.
The power increased from a Super Saiyan 7 is much higher than a Super Saiyan 6, as Vegeta where he first achieved the transformation, was able to defeat Goku when he was Super Saiyan 6. And all the techniques used become different, as the Final Flash will turn into the Ultimate Flash, and the Kamehameha will turn into the instant
Creation And Story How They Used It 
In the fan-made Battle of the Gods 2, where Goku defeated both Beerus and Whis, Vegeta refused to be surpassed by Goku with such an amazing gap of power. After training in the Time Chamber for nearly 3 Years, Vegeta discovered a new transformation, Vegeta thought he is ready to face Goku one-on-one. After Vegeta stating that he wants to face Goku while Super Saiyan 6, Goku responded and went to SSJ6 according to his wishes, Vegeta then skipped the Super Saiyan 6 Transformation and went on the Super Saiyan 7 Transformation, easily beating Goku. Vegeta, who thought he achieved his dreams of becoming the ultimate warrior in the universe, was shattered, when he knew that Goku was able to take the same form Vegeta took after training for 3 Years in the Time Chamber, the battle was tied as neither Goku nor Vegeta were able to finish off the other, but Goku, after Powering Up to the Very Limit, launched a Kamehameha on a weakned Vegeta, thus ending the battle After A Weakend SSJ7 Vegeta He Snapped To Doing A Inraged Ultimate Flash Goku Uses Kaioken Using A Instant Kamehameha! After The Beam Clash Both Train Harder