Precision is the fraction of relevant instances among the retrieved instances.
It’s asking the question:
How many selected items are relevant?

Recall is the fraction of relevant instances that have been retrieved over total relevant instances.
It’s asking the question:
How many relevant items are selected?

Recall and Precision are inversely related.

Example:

On a 1000 movie hard disk which had 200 thriller movies, all the movies which belonged to ‘thriller’ genre was separated out and 70 were listed out. Out of 70 that were separated, 40 were relevant. Find Precision and Recall.

A = number of relevant records retrieved = 40
B = number of relevant records not retrieved = 200 – 40 = 160
C = number of irrelevant records retrieved = 70 – 40 = 30

Precision = A / (A+C) = 40 / (40+30) = 40 / 70 = 0.5714 = 57.14%

Recall = A / (A + B) = 40 / (40+160) = 40/200 =  0.2 = 20%