By Lisa Respers France, CNN

(CNN) -- Taylor Swift launched her concert tour Tuesday talking about her reputation.

The superstar singer kicked off her Reputation Stadium Tour in Glendale, Arizona, and opened up a bit about her trademark snake imagery.

"A couple of years ago, someone called me a snake on social media, and it caught on," Swift said, according to video tweeted by a fan. "Then, a lot of people were calling me a lot of things on social media. And I went through some really low times for awhile because of it. I went through some times when I didn't know if I was going to get to do this anymore."

Swift apparently was referring to an episode in 2016 when she clashed with rapper Kanye West after he called her a "b" and took credit for her fame in his song, "Famous."

Taylor Swift's biggest beefs

Things got even more heated when his wife, reality star Kim Kardashian West, shared a video on social media of a call between West and Swift in an attempt to prove Swift knew about the West lyric and had signed off on it.

Kim Kardashian tries to prove Taylor Swift lied

Kardashian West also tweeted at the time about National Snake Day, which some interpreted as being aimed at Swift.

"Wait it's legit National Snake Day?!?!?They have holidays for everybody, I mean everything these days," Kardashian West wrote.

On Tuesday, Swift talked to her concert audience about how she's embraced the snake imagery, which has figured prominently in the music videos for her "Reputation" album and her shows.

"I wanted to send a message to you guys that if someone uses name-calling to bully you on social media, and even if a lot of people jump on board with it, that doesn't have to defeat you," she said. "It can strengthen you instead."

She continued as her audience cheered.

Taylor Swift and snakes: The backstory

"And I think something that came out of it that was good is that I learned a really important lesson that I've been telling you from the stage for about 10 years, but I never had to learn it so harshly myself," Swift said. "And that lesson has to do with how much you value your reputation."

"I think that the lesson is that you shouldn't care so much if you feel misunderstood by a lot of people who don't know you, as long as you feel understood by the people who do know you -- the people who will show up for you, the people who see you as a human being," she told her fans. "So thank you, thank you, thank you for taking the time to get to know me, for showing up for me, for seeing me as a human being."

Swift also on Tuesday apparently had some words of thanks on social media for a former rival. In an Instagram post, the pop star shared an image of an olive branch and a letter, along with the superimposed title, "Thank you Katy."

Many Swift enthusiasts, including a fan site, interpreted the gift as Katy Perry's attempt to quell the apparent animosity between the two superstar singers -- perhaps on full display in Swift's 2014 song, "Bad Blood" -- on what was to be a huge night for Swift. Perry made no mention of it on social media.