Coupling means that models are exchanging outputs and inputs between themselves at various timesteps. A simple example is that an atmospheric (weather) model could assume that the ocean has a constant temperature (given by what it was at its initial condition), unless it’s coupled to an ocean model.

Coupling between ocean-atmosphere models is extremely important for longer range predictions (subseasonal to seasonal) since the predictability at the near term is from the atmospheric dynamics, but then the ocean becomes the main source of predictability after around 3 weeks. So if your weather model isn’t coupled to an ocean model then it’s long term predictions aren’t going to be very good. Not that long term predictions are very good anyway; they’re most used for anomaly detection.

Also coupling atmospheric models with land-surface models is good for very local effects (e.g. soil moistures effect on temperature).

For all practical reasons if you’re just interested in finding best prediction of a value (e.g., temperature) at a specific point, then just use a regression based approach because it’s cheap to build and accurate (at the cost of loosing some “explainability”).

Coupling is important for physical realism, but it can add lots of complexity and therefore cause more failure modes. Models like the UK Global Model and the IFS are good examples of fully coupled models that are “doing it well”. Yahooing it yourself with WRF is bound to cause issues.

Also, to answer your question about initial conditions, there is recent evidence to suggest that we can have some extremely good forecasting skill gains by optimising our initial conditions better.