Gi and No-Gi are two forms of Brazilian Jiu-Jitsu. Gi Jiu-Jitsu is grappling with the use of a traditional Gi, that allows you to grab the clothing of your opponent. No-Gi is grappling without the traditional uniform, instead you wear shorts and a rash guard. In No-Gi you cannot grab your opponent’s clothing.
To be a complete BJJ player, you should train on both forms. Marcelo Garcia, a world class BJJ player, is a professional on both Gi and No-Gi Jiu-Jitsu. He started as a No-Gi brown belt, having built a strong base in Gi Jiu-Jitsu first. Usually if you start training in majority without the Gi, then you will have a harder time adapting to the Gi Jiu-Jitsu. The Gi Jiu-Jitsu in some ways is more complex with all the grips, but No-Gi also has other aspects which are not found in the Gi (for example the more brabo chokes, guillotines, footlocks than in the Gi).
Gi & No-Gi Jiu-Jitsu
Dress
In Gi, you will of course wear a BJJ Gi. In No-Gi, you wear shorts and a T-shirt or rash guard.
Grips
The Gi Jiu-Jitsu has a huge amount of grips on both the jacket and pants. The most common jacket grip is the collar/sleeve grip. The grips allow you to have great control on the fight and to submit your opponent using their or your own Gi. It allows a much smaller opponent to control a bigger one. In No-Gi Jiu-Jitsu, you have more wrestling based grips, such as the neck and grabbing the joints of the body. It is harder to control, as your grips may slip or power out the opponent.

Strategy
Gi and No-Gi Jiu-Jitsu: What are the differences? No-Gi BJJ has a faster pace. Gi slows things down due to the natural friction of the garments.
While the Gi and No-Gi are very similar, the way both styles evolved is very different. In Gi Jiu-Jitsu, numerous grips and the Gi itself meant that there are a lot of set ups done on the Gi materials used, like lapel or worm guard (which is impossible in the No-Gi Jiu-Jitsu). In No-Gi Jiu-Jitsu, you focus more at taking your opponent’s back because mounting in No-Gi has limited submissions, and in the back position, rear naked choke and other options can be done. You will find No-Gi players using more guillotines and brabo/darce chokes as well as using more foot locks.
It is hard to say what is more technical as both styles are different. Also, No-Gi players with smaller body-builds most likely submit to the bigger ones, taking the back is a great way of doing that.

Rules
Most No-Gi Jiu-Jitsu tournaments have slightly different rules from Gi Jiu-Jitsu. IBJJF rules do not allow heel hooks for Gi Jiu-Jitsu, while ADCC (the biggest No-Gi Jiu-Jitsu tournament) allows them.
Marcelo Garcia is a multiple Gi IBJJF world champion and a four-time ADCC No-Gi Jiu-Jitsu champion.