Sage Mode is the result of using natural energy along with a ninja's normal chakra in perfect balance to drastically empower a ninja's abilities.
Senjutsu refers to a specialized field of jutsu that allows the user to sense and then gather the natural energy around a person. Senjutsu practitioners can then learn to draw the energy of nature inside of them blending it with their own chakra, adding a new dimension of power to the sage's chakra, resulting in the creation of "senjutsu chakra". This chakra cannot be seen by anyone other than those who have been trained in senjutsu.
This new chakra enables the user to enter an empowered state called Sage Mode, which can then drastically increase the strength of all ninjutsu, genjutsu, and taijutsu. A person who is able to use senjutsu is called a sage. It would seem that it stems from the toads of Mount Myƍboku, as only Shima, Fukasaku, Jiraiya and Naruto have been seen using it. Gamakichi and Gamabunta also seem to be familiar with it. A prerequisite to being able to use Senjutsu is that the user must have a great reservoir of chakra themselves in order to manipulate the natural energy.

Advantages
The user's physical strength, speed, stamina, and durability dramatically increase, to the point where they could fall face first into a bed of spikes and receive no injury nor feel pain whatsoever.
The user's ninjutsu, genjutsu, and taijutsu become more powerful.
The user can harness the natural energy surrounding them, turning it into an extension of their body, which increases the reach of their attacks.
The user gains the ability to sense chakra around them.

Disadvantages
If the user draws in too much natural energy in the attempt to initiate Sage Mode, they run the risk of transforming into a toad, then into stone. If the transformation is completed, it cannot be reversed.
In order to gather enough natural energy to initiate the transformation into Sage Mode, the user must remain perfectly still. Because of that, the user can be an easy target for an opponent.
Because the user needs to move during combat, the Sage chakra cannot be replenished, which means the user can't stay within this state for extended periods of time.
The second and third weaknesses mentioned above can be bypassed through the Sage Art: Amphibian Technique, where one Sage gathers chakra for another or as in Naruto's case, shadow clones can be used for the same purpose.
After Sage Mode has ended, the user appears to experience exhaustion.

Users
Shima
Fukasaku
Jiraiya
Naruto Uzumaki

Classification
Senjutsu

Class
Supplementary