Deuterium-tritium fusion reaction is the one that releases the majority of energy in a hydrogen bomb. Fusion reaction can only occur if the reactant is in the thermonuclear plasma state (i.e. the nuclei are free). That requires extremely high energy (i.e. extremely high temperature), which can be supplied only (in the case uncontrolled reaction, i.e. explosion is necessary, given the constraints) by a nuclear fission explosion, which is much more easily attained (being detonated by conventional explosives itself).
So, the fission bomb is the detonator part of the fusion bomb.
The main fusion reaction is:
H(1,2) + H(1,3) -> He(2,4) + n(0,1) + 17.6 MeV
A lot of energy is released (and potentially lost) as a kinetic energy of the fast neutrons that are a product of the reaction. In order to enhance the released energy of the explosion, by capturing the runaway neutrons and replenishing the supply of tritium for the reaction, there is an additional fission reaction, involving lithium-6.
Li (3,6) + n (0,1) -> H (1,3) + He (2,4) + 4.9 MeV.
For the sake of completion, all four reactions that hydrogen bomb is based on are:
H(1,2) + H(1,2) -> He(2,3) + n(0,1) + 3.3 MeV
H(1,2) + H(1,2) -> H(1,3) + p(1,1) + 4 MeV
Li (3,6) + n (0,1) -> H (1,3) + He (2,4) + 4.9 MeV.
H(1,2) + H(1,3) -> He(2,4) + n(0,1) + 17.6 MeV
Initial fission reaction is omitted since it releases very small amount energy compared to the four reactions above. As evident, most of the energy is released in the fourth reaction, and the rest of the reactions have the main purpose of (re)generating tritium for the fourth reaction. Since it uses fission as a detonator, and involves both fusion and fission in the main energy generating process, hydrogen bomb is referred to as a fission-fusion-fission bomb.
Addendum: unlike hydrogen bomb, which seeks to maximize dissipated energy (kinetic energy of the charged nuclei products, blast, heat), neutron bomb seeks to maximize the kinetic energy of generated fast neutrons, so it does not contain lithium, and relies on the first, second and fourth reaction. Since neutrons interact with matter with much smaller frequency, there is no significant damage to structures, but damage to living tissues is fatal. That makes neutron bombs appropriate for tactical use.