We identify localizable entanglement (LE) as an order parameter for measurement-induced phase transitions (MIPT). LE exhibits universal finite-size scaling with critical exponents that match previous MIPT results and gives an operational interpretation connecting MIPTs to classical percolation. Remarkably, we find that LE decays exponentially with distance in the area-law phase as opposed to being essentially constant for the volume-law phase thereby, discover an intrinsic length scale ${\xi }_E$ that diverges at the critical measurement probability $p_c$. While classical percolation transition captures successful transport across a network, MIPT as characterized by LE can be interpreted as quantifying the amount of quantum teleportation between two given nodes in a quantum circuit. Building on this insight, we propose a two-ancilla protocol that provides an experimentally accessible readout of entanglement redistribution across the transition.