p = "Passenger". its the North American tire sizing designation sometimes you'll see like T, or LT for trucks or light trucks.
205 (width of tire) also known as the "section width". What this is, is the width of the tire in millimeters from the widest points. (sidewall to sidewall).
65 is height also known as " Aspect Ratio". Actually techniclly its calculated by dividing the section height by the section width and multiplying by 100. (In this example, the sidewall will be 65% of 205)
R means that its a radial tire. Thats how its constructed.
15 = rim size. 15 inch rim.
Sometimes you'll see like a P infront of it
Then theres the speed ratings. Different Letters mean different speed ratings. Dont know them off the top of my head. Z rated tires are rated over 150 mph. Dont know if there the top or not.
N 87 mph 140 km/h
P 93 mph 150 km/h
Q 99 mph 160 km/h
R 106 mph 170 km/h
S 112 mph 180 km/h
T 118 mph 190 km/h
U 124 mph 200 km/h
H 130 mph 210 km/h
V 149 mph 240 km/h
Z >149 mph >240 km/h (how much greater is not specified and may vary per tire)
W 168 mph 270 km/h
Y 186 mph 300 km/h