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1.
Initialism for "speak with you later". It's a way for the speaker/writer to politely indicate that the conversation has come to a natural close or that he needs to focus on an activity other than the conversation but does want to finish the conversation later or will get back to the listener/reader later with the desired information.

It's better than "talk to you later" (TTYL) because SWYL implies actual dialogue or conversation between the two people ("speak with you" vs. "talk to you").

It also can be a more formal or businesslike way to bring an IM, email, or SMS text conversation to a close.
Him: Alright, I gotta hit the gym, but let's finish chatting about it more when I'm done.
Her: okay, SWYL.
by 1102MTD November 27, 2011
 
2.
term meaning "sex with you later"
bye, swyl
- ok
by James Warberyagermanjensen September 17, 2009