People do 'data assimilation' all day long, usually unconsciously.
We use our lifetime of experience to anticipate what will happen,
but we know that the future is uncertain, so we keep observing what's actually happening,
and update our prediction if necessary.
People have developed equations which describe this process,
which can be applied to systems which are too large and complex
for a human mind to comprehend all at once.
Earth is one example.

Valuable information about the current conditions in the atmosphere, ocean, land, and ice
comes from two sources; recent observations and mathematical equations
which describe those Earth components.
But both contain approximations and limitations
arising from limited resources for measuring and calculating,
as well as limits in our understanding.
Data assimilation is a method for extracting and combining the information
into a more coherent, accurate whole, discarding the errors in each source
as much as possible, and describing the remaining errors
so that we know how much confidence to have in the 'coherent whole',

The ability to create better pictures of the Earth's systems enables us
to improve our equations and our observations, leading to even better pictures,
in a 'virtuous cycle' of improving understanding.