"a call to drink to someone's health," 1690s (but said by Steele, 1709, to date to the reign of Charles II), originally referring to the beautiful or popular woman whose health is proposed and drunk. The custom apparently has its origin in the use of spiced toast (n.1) to flavor drink, the lady being regarded as figuratively adding piquancy to the wine in which her health was drunk.
The custom itself is much older than this word for it, and the expectation of a bit of toast in a mug of ale at a tavern is well attested in many 17c. drinking songs, though none of them seems to give a reason for it.
Steele's story ["Tatler," No. 24] is that an (unnamed) beauty of the day was taking the cold waters at Bath, when a gentleman dipped his cup in the water and drank it to her health; another in his company wittily (or drunkenly) replied that, while he did not care for the drink, he would gladly enjoy the toast. Meaning "one whose health is proposed and drunk to" is from 1746. Toast-master attested from 1749.