The DIESIS project  gives the following definition:
Open Modelling Interface (OpenMI) is a modelling standard emerged
from the domain of water system simulation. The standard is developed
and maintained by the OpenMI Association (http://www.openmi.org).
From their web site OpenMI describes itself as:
“The OpenMI can be described at two levels.
At the users level, the OpenMI provides a standard interface, which allows
models to exchange data with each other and other modelling tools on a
time step by time step basis as they run. It thus facilitates the modelling of
process interactions. The models may come from different suppliers, represent
processes from different domains, be based on different concepts,
have different spatial and temporal resolutions and have different spatial
representations including no spatial representation. A useful analogy is to
consider the OpenMI as the modelling equivalent of a USB cable.
At the IT level, OpenMI standard is a software component interface definition
for the computational core (the engine) of the computational models
in the water domain. Model components that comply with this standard
can, without any programming, be configured to exchange data during
computation (at run-time). This means that combined systems can be created,
based on OpenMI-compliant models from different providers, thus
enabling the modeller to use those models that are best suited to a particular
project. The standard supports two-way links where the involved models
mutually depend on calculation results from each other. Linked models
may run asynchronously with respect to timesteps, and data represented
on different geometries (grids) can be exchanged seamlessly.
The OpenMI standard is defined by a set of software interfaces that a
compliant model or component must implement. These interfaces are
available both in C# and Java.”
Other International Definitions
United Nations’ Definition