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each node in a connectionist network has an activation level. this is generally a floating point number between 0 and 1. the activation level varies with time. a connection (which, as you recall, is one-way) from node Alfred to node Arnie has a weight attached to it. the weight is another floating point number; this time it's generally between -1 and 1. Arnie's activation level for the next time tick is found using his activation from the current tick and the product of Alfred's activation level and the Alfred-to-Arnie connection weight.

(italics indicate subscript...) in a simple connectionist model, Arnie's activation level is this:

aarnie = f(Saalfredwalfred->arnie)

..where a is activation level, f is some function, often a function whose shape is sigmoidal, S is a sigma, and w is a connection weight.