To my knowledge, Monogamy means that If particle A and B are in a maximally entangled state, for example one of the Bell states, then particle A or B can not have entanglement with the third particle C. This can be extend to more particle's systems. For example, for GHZ states, the entanglement between all possible bipartitions like A-BC are equal to one (by using normalized negativity), so A cannot have entanglement with any other particle D. This is true for any other two bi partitions.
In the material below I define the Bell states, the GHZ state and normalized negativity.
Bell state: Bell states are maximally entangled states for two particles. your particles can be Qubits (the Hilbert space of each one is two dimensional space), or they can be Qudits (the Hilbert space of each one is a d dimensional space). Here you can see Bell states for two qubits:
\begin{eqnarray}
\vert\phi_{\pm}^{AB}\rangle &=&\frac{1}{\sqrt{2}}(\vert 0^{A},0^{B}\rangle\pm\vert 1^{A},1^{B}\rangle)\:,\nonumber\\
\vert\Psi_{\pm}^{AB}\rangle &=&\frac{1}{\sqrt{2}}(\vert 0^{A},1^{B}\rangle\pm\vert 1^{A},0^{B}\rangle)\:.
\end{eqnarray}
GHZ state: GHZ states, or Greenberger-Horne-Zeilinger states, are states with at least 3 particles. There exist certain kind of entanglement between their bipartitions. The GHZ state of M particles is defined as
\begin{equation}
\vert\Psi_{GHZ}\rangle_{M} =\frac{1}{\sqrt{2}}\left(\vert 0\rangle^{\otimes M} +\vert 1\rangle^{\otimes M}\right).
\end{equation}
For example, if M=3,
\begin{equation}
\vert\Psi_{GHZ}\rangle_{3} =\frac{1}{\sqrt{2}}\left(\vert 000\rangle +\vert 111\rangle\right).
\end{equation}
Here the entanglement between any of $\vert\Psi_{GHZ}\rangle_{3}$ bipartitions is equal to 1 and if we trace about one of the qubits there will be no entanglement between the remaining two qubits.
Normalized Negativity: The Peres-Horodecki criterion is one of the measures of multipartite entanglement, which is called Negativity and can be defined as
\begin{equation}
N(\rho)=\frac{\Vert\rho^{T_{B}}\Vert_{1}-1}{d-1},
\end{equation}
where $ \rho^{T_{B}} $ is partial transpose of state $ \rho $ with respect to partition $ ``B" $ in a $ d\otimes d^{'} $-dimensional quantum system $ (d\leq d^{'}) $, and $ \Vert \cdot \Vert $ is the trace norm. The equivalent definition of negativity is based on negative eigenvalues of $ \rho^{T_{B}} $
\begin{equation*}
N(\rho)=\frac{(\sum_{\lambda_{i}}|\lambda_{i}|)-1}{d-1}
\end{equation*}
