I read this one in my dictionary (Chambers, 11th edition).  Apparently, a Handsel is an inaugaral gift of some kind, such as a coin in the pocket of a new coat or in a new purse.  Also the first use of something or a first instalment, or something thought of as a beginning or inaugaration.

And apparently, Handsel Monday is, especially in Scotland, the first Monday after New Year, when handsels were given.  I forgot this year; might try it next year.