When you hover over the ✔ mark/icon, a tooltip pops up:
Click to set this answer as your accepted answer; click again to toggle
If you didn't click the accept button but instead upvoted, you would get a little box that says
don't forget you can mark this as the accepted answer by clicking its check mark
(The system stops showing this reminder after a certain rep threshold.)
Also, you'd see a lot of other questions on the site having big green checkmarks, so I think that's another clue you could accept answers. If you don't accept answers, the profile page starts to nag you also.
It's also mentioned in the FAQ:
How do I ask questions here?
As you see new answers to your question, vote up the helpful ones by clicking the upward pointing arrow to the left of the answer. Answers are normally sorted by vote score so the most highly voted answers float to the top. Other users will also vote on the answers to your question.
When you have decided which answer is the most helpful to you, mark it as the accepted answer by clicking on the check box outline to the left of the answer. This lets other people know that you have received a good answer to your question. Doing this is helpful because it shows other people that you’re getting value from the community. (If you don’t do this, people will often politely ask you to go back and accept answers for more of your questions!)
There's also an accept rate on every person's info box on the questions they ask:
Because all these things exist, I have always thought that the additional clarification you ask for isn't needed... I've answered meta questions stating this before. I used to be very steadfast in my position... however you as a new user bringing it up makes me rethink my position... I have always seen longer term users complaining that new users didn't know how to accept, and thought they were wrong. Now that I see a new user saying "I didn't know how to accept an answer", I think that maybe I have been wrong.
On the other hand... you did figure it out on your own, without the need for additional help :-)