Soul Resonance

Soul Resonance (魂の共鳴, Tamashii no Kyōmei; Literally meaning "Resonance of the Soul") is a special technique used by Meisters and Weapons, in which, they synchronize their Souls wavelength. By doing so, they can release highly powerful techniques and, more often than not, change the tide of a battle.

Resonating Souls
Resonating Souls is the foundation of using the Soul Resonance technique and are how most partners are matched up. The souls of both Meister and Weapon should compliment one another for the best result. Resonating souls with partner's souls that are too similar can result in feedback effect, hurting both parties and resulting in failure in technique or form of combat.
Resonating requires both meister and weapon to be calm and of one mind. Should one of the soul not be in sync, techniques can not be performed. If a technique is being used and one soul loses focus, the technique will lose power or direction, as seen with Maka losing her footing when she lost focus while using Witch Hunter against Sid. Common reasons for soul's not to sync are fear, arguing, stress, etc. In addition to those factor, Maka couldn't match wavelengths with Soul, much less hold him, after he was first infected with Black Blood though this could be due to the training that Dr. Stein had them underwent before they had their next battle.
It is possible to resonate with more that one soul at a time, but it is noted to be a hard technique to control and use effectively. Kid and Kilik are the only two Meisters that have been noted to wield and resonate with more than one soul at once.

Shinigami's Explanation

In a conversation with Kid, while watching Maka and Black Star fight Stein, Shinigami describes Resonating Soul and the techniques that result are like playing an electric guitar with and without an amp.
“ A Meister and a weapon are like an electric guitar and an amp."
"The sound (soul wavelength) that comes from an electric guitar (Meister) by itself is rather faint..."
"But when you connect an amp (Weapon) to it, the soul wavelength is amplified, giving it a lot of power."
”
—Shinigami, Episode #5 "Shape of the Soul - Enter the Ultimate Meister, Stein?"

Chain Resonance
Chain Resonance (or Team Resonance), just as it would indicate, is a kind of Resonance that involves a team of Meisters matching their wavelengths with one another in order to empower each other. It is extremely difficult to maintain, unless all the team can easily keep their souls on a balanced level. There is no set number to the amount of meisters required to perform the Chain Resonance, but it is more powerful yet more difficult in a larger team. Also, Chain Resonance seems to work best with weapon's of similar elements, such as, Harvar and Pot of Thunder.
During the battle for Brew, Soul played the piano in order to give the resonance a rhythm to follow, establishing a much more stable connection which allowed the meisters to fully concentrate on the opponent rather than on the complex balancing issues.

Other forms of Resonance
Scream Resonance
Scream resonance is the form of resonance that Crona and his/her Demon Sword Ragnarok use. When initiating the resonance, the mouth that appears on Ragnarok (as a weapon) opens wide screaming out a loud sound wave. This sound wave can cause internal damage to an opponent and even other weapons, shown when in contact with Soul causing him pain even in weapon form. Beside the piercing sound wave, this resonance is just the same as a normal Soul Resonance.

Soul Menace
Soul Menace is a form of "self resonance" with one's soul, meaning that the user's own soul becomes powerful enough that it is not restricted to using the amplification of a weapon in order to attack. This allows the user to use attacks that cause damage to a target internally. This can even affect a user of the Black Blood, causing damage and even causing the blood to reject it's host.