Beer's Law is typically expressed as A=(e)bc only the (e) is actually the greek letter epsilon I can't type (either because there's no function for it or I'm just not smooth enough).
A = absorbance, which is a function related to the transmittance. Transmittance is how much light of a certain wavelength actually passes through the solution. Absorbance is a transformation of transmittance - the spectrophotometer does the math for you (even professionals don't usually know the details, spectrophotometers always present their results to you in terms of absorbance). Absorbance is more useful than transmittance because it has a LINEAR relationship to concentration, as you've noted.
(e) = molar absorbtivity coefficient (or constant), which is a constant that is different for each solution. This constant is the slope of the line in a typical Beer's Law plot.
b = the thickness of the path the light has to take passing through the solution... because most spectrophotometers always use a standard sized test tube (say the width is always 1cm for all measurements) this is essentially NOT a factor and can simply be omitted from the equation. Sometimes people call b "l" for length, but those people are lonely and should adopt a pet. Something affectionate, like a cat or a dog, not like a fish or a lizard.
c = the concentration of the solution; note that any units can be used so long as they are linearly based (i.e. you can't use pH or a logarithmic measure of concentration, but ppm, %, molarity, g/mL, etc. are all fine) AND so long as they MATCH THE UNITS OF (e). Normally you're just figuring out (e) for yourself so it's whatever units you feel like calculating it in. Typically real world chemists would be working in either ppm (for super dilute stuff, which is often what spectrophotometry is used for) or in M (molarity).
So yes, it's typically just linear, as A=(e)C meaning absorbance is directly proportional to concentration (remember (e) is just a constant, making it the slope of the line relating A to C). Also, Beer's Law graphs pass through the origin. My undergrads ALWAYS screw that up even after I warn them that they're going to.