If you don't know what the term width refers to, please read first this answer.
As mentioned there, the decay width Γ of particle is directly related to its decay lifetime: the faster the particle decays, the larger its decay width. In general, a particle can decay in several "modes", also called "decay channels". For example, a Z boson can decay into a pair of neutrinos, a pair of charged leptons, or a pair of quarks (i.e., all the standard model fermions lighter than mZ/2). The probability for a Z to decay into a neutrino pair is about 20%, into a pair of charged leptons (electrons, muons, or taus) is about 10%, and into a pair of quarks (u,d,c,s,b) is about 70%. These probabilities are also called branching fractions or branching ratios.
The partial width of a given decay channel is nothing but the product of the total width Γ and the corresponding branching ratios. For example, the partial width of the Z into neutrinos (also called invisible width of the Z) is 20% x 2.5 GeV, i.e. about 500 MeV. The sum of the partial widths of a particle equals the total width Γ.