The y-intercept is the value of the function when the independent variable, x is 0.  Often this position on the graph is imposed or determined by the problem solver for convenience.  It represents an arbitrary starting point of a model is equal to zero (0).  It is this zero point of the independent variable that is imposed by the person(s) solving the problem. When, for example, the independent variable is time, t it would mean that any time period or increment after that starting point is positive and any time period or increment before is negative.

If one is interested in the depreciation of the value of an item with time since 1985, then one can use 1985 as the starting time and so define it as 
t = 0. So a date of 1991 would be (1991 - 1985) t = 6 and a year of 1980 would be (1980 - 1985) t = -5. Note we subtract the date or time being evaluated from the defined date when t = 0, 1985.

The y-intercept is the function calculated when the independent variable is equal to zero (0) and often is interpreted as the initial value of the function or the starting value of the function or the value of the function when t or x = 0.

For  most functions the y-intercept is easily determined.

When you sketch or examine a function in this text, the y-intercept becomes a useful point on the graph and if given usually make finding the formula for the model easier.