What's the difference between the meanings of these two sentences?
My homework has to do with last week's activity.
My homework has something to do with last week's activity.
Use of "something" here implies uncertainty - it suggests that you know that there's a connection but you're not sure what it is. The other time you would use "something" like this is when you want the person you're speaking to to guess what the connection is. In both cases, the use of "something" begs the question "What is the "something"?"
This is because the word "something" is very vague - it's saying "there is a thing" but it's not telling the listener anything about what it is.
"My homework has to do with last week's activity." still invites people to try to guess the connection, but not as "strongly".