Basically, 戒め is something that firmly restricts or binds yourself. 戒【いまし】め here means lesson or warning in simple English. More difficult words such as aphorism or wisdom may fit better. So
#自分への戒め is as simple as "a lesson for myself."
戒め is a very old-sounding word, but recently we see 戒め more often in the internet, because this has been a net slang since several years ago. 戒め is typically used at the end of sentences in the form of
(戒め). Search 戒め at twitter.com and you can see hundreds of wild and peculiar usage of this. This page explains the etymology, but I think many people are using 戒め without knowing the origin.
Basically 戒め is used when they want to say "I realized this" or "I shouldn't have done this", but people use this pretty loosely and jokingly.
Of course you can use this idiom to write something serious about self-discipline, but even seeing the hashtag
#自分への戒め, I can see very few people use it seriously today.