proportion of explained variance

Hello everyone,

One of the terms I can not really make sense of is "proportion of explained variance" It comes up in the context of multiple linear regression or factor analysis for example. Let's say the term indicates how much of the variance in y is explained by the predictor variable x. That's how it is used in psychology research.

I imagine sth like a column of y scores and an adjacent column of x scores. Would 100 % "explained variance" imply that when x for example doubles y doubles too or how can I imagine the relation between x and y when one talks about explained variance ?

I feel stupid and would be thankful for someone to help me with this and maybe other questions.
Cheers !