Almost synchronous refers to a transmission where the sending and receiving devices are synchronized, but set to different clocks. Although the bits may not arrive in the same time slot as they were sent, as long as they arrive within a certain, defined range, the transmission is said to be plesiochronous.
The term is used in the "Plesiochronous Digital Hierarchy" (PDH), the widely-used system in which the transmissions from one continent (such as North America) are internetworked with transmissions in other continents (such as Europe) by making small adjustments in the differing data rates between the systems. The European and American versions of the PDH system differ slightly in the details of their functions, but the principles are the same.
A plesiochronous situation can arise when two systems have slightly different clock readings over time. In such circumstances, one of the components, or a third system, would need to notice the mismatch and make some compensating adjustments, such as repeating or deleting a data packet or frame.