A vehicle tires dimension has been expressed as "27×7.75 R15". What does the numbers indicate ?

In English/imperial measurement, that means the tire is 27 inches in diameter, 7.75 inches wide, Radial type and wrapped around a 15-inch wheel. 

These letters are the standards to qualify a tire, 27x7.5 R15 means, 27 is the width, 7.5 is the height of the sidewall and R15 diameter

the tires dimensions expressed  as for example: 270/75R15 and its mean as shown below:

270  is the width of the tire measured in millimeters from sidewall to sidewall.(three digit number) 

75  is  the ratio of the height of the tire's cross-section to its width( two-digit number after the slash mark in a tire size is the aspect ratio).

R The letter "R" in a tire size stands for Radial, which means the layers run radially across the tire.

15  is the size of the wheel measured from one end to the other. It tells us the size of the wheel that the tire is intended to fit. 

sometimes we found letter p in the beginning of the dimension(P270/75R15)  tells us the tire is a P-Metric tire, referring to tires made to certain standards within the United States, intended for Passenger vehicles.

The letter or letters in the beginning of the tire size indicate the type of service and the type of vehicles that can use these tires. For example, a "P" at the beginning of the tire size means that the tire should be used on passenger vehicles, such as cars, minivans, sport utility vehicles and light duty pickup trucks.