Learn English – What does it exactly mean

I think "go" here is an abbreviated version of "go together". "Go together" is an idiom meaning "are well-suited to each other", "are compatible", or "make a good pair". You might say, "This lamp and this chair go together" meaning that you think the styles of each are such that they are attractive when placed next to each other. We often say that two people "go together" meaning that we think that they make a good couple. (Perhaps I should clarify that we also say "those two people go together" meaning that they are involved in a dating relationship, which phrase, I think, has totally different origins but ends up being a closely-related idea. The two ideas go together. :-)

The word "go" can have other meanings that would fit here, like "work", as in, "Does this car go?" meaning, "Does it work correctly, does the engine run, etc.?" But the next sentence is "If they match", so I think the writer is stating the same idea in two different ways for emphasis, "If they go [together]. If they match."

Base state is a term used in statistics.

We have a measurable quantity, in this case the temperature of the sea.
We have an effect upon that quantity, El Nino increases the temperature and therefore the rainfall.

Each El Nino event may raise the temperature by a different amount. However, if the starting point from which the temperature is being raised - the Base State - is higher (due to global warming) then the peak caused by El Nino will be higher.

In effect, put very simply, the whole temperature graph goes up a bit.

The base state is the value of a variable before it is altered before an external event and to which it returns after that event.